What is the angular velocity of the second hand on a clock? (Hint: It takes the second hand 60 seconds to rotate 2π radians. Divide the number of radians by the number of seconds so that your answer has units of radians/second.)

Answer:

6613.87 lbs

Explanation:

1.2 m³ = 1200000 cm³

Mass = Density * Volume

M = (2.5 g/cm³) * 1200000 cm³ = 3000000 g

1 lb = 453.592 g

3000000 g * (1 lbs / 453.592 g) = 6613.87 lbs

The mass of the rock is 6613.87 lbs.

Mass is the quantity of matter in a physical body and the weigh is used to measure ascertain the heaviness of by or as if by a balance.

Given that volume of the rock is 1.2 meter cube and density is 2.5 gram/cm cube. The height of the rock is 4 feet. The mass can be calculated as given below.

Mass m = Density w [tex]\times[/tex] Volume v

Substituting the values in the above equation.

[tex]m = 2.5 \;\rm g/cm^3 \times 1.2\;\rm m^3[/tex]

[tex]m = 2.5 \times 1.2 \times 1000000[/tex]

[tex]m = 3000000\;\rm g[/tex]

The mass of the rock is 3000000 g. We know that

[tex]1\;\rm lb = 453.592\;\rm g[/tex]

[tex]1\;\rm g = \dfrac {1}{453.592} \;\rm lb[/tex]

Now convert the mass (grams) into mass (lbs).

[tex]m = \dfrac {1}{453.592}\times 3000000\;\rm lbs[/tex]

[tex]m = 6613.87 \;\rm lbs[/tex]

Hence we can conclude that the mass of the rock is 6613.87 lbs.

To know more about the mass, follow the link given below.

https://brainly.com/question/15959704.

Answer:

0.2448 point²

Explanation:

1 gry = 1/10 line

1 line = 1/12 inch

=> 1 gry in inches = 1/10 * 1/12 = 1/120 inch

=> 1 inch = 120 gry

1 point = 1/72 inch

=> 1 inch = 72 points

Therefore,

120 gry = 72 points

=> 1 gry = 3/5 point

Therefore,

1 gry² = (3/5)² point²

1 gry² = 9/25 point²

This means that 0.68 gry² will be:

0.68 gry² = 0.68 * 9/25 point²

=> 0.68 gry² = 0.2448 point²

The area of 0.68 gry2 is 0.2448 point2.

Given that A gry is an old English measure for length, defined as 1/10 of a line. We can write this as given below.

[tex]1 \;\rm gry = \dfrac {1}{10}\;\rm line[/tex]

A line is another old English measure for length, defined as 1/12 inch. We can write this as given below.

[tex]1 \;\rm line = \dfrac {1}{12}\;\rm inch[/tex]

Thus the value of 1 gry in inches will be,

[tex]1 \;\rm gry = \dfrac {1}{10}\times \dfrac {1}{12} \;\rm inch[/tex]

[tex]1 \;\rm gry = \dfrac {1}{120}\;\rm inch[/tex]

[tex]120 \;\rm gry = 1\;\rm inch[/tex]

A common measure for length in the publishing business is a point, defined as 1/72 inch. We can write this as given below.

[tex]1 \;\rm point = \dfrac {1}{72}\;\rm inch[/tex]

[tex]72 \;\rm point = 1 \;\rm inch[/tex]

Now we can equate the values of 1 inch, we get the expression as,

[tex]120 \;\rm gry = 72 \;\rm point[/tex]

[tex]1 \;\rm gry = \dfrac {72}{120}\;\rm point[/tex]

[tex]1 \;\rm gry = 0.6 \;\rm point[/tex]

[tex](1\;\rm gry )^2 = (0.6 \;\rm point)^2[/tex]

[tex]1\;\rm gry ^2 = 0.36 \;\rm point^2[/tex]

We have the value of 1 gry2 in terms of point2. Thus,

[tex]0.68 \;\rm gry^2 = 0.68 \times 0.36 \;\rm point^2[/tex]

[tex]0.68\;\rm gry^2 = 0.2448 \;\rm point^2[/tex]

Hence we can conclude that the area of 0.68 gry2 in points squared is 0.2448.

To know more about the area, follow the link given below.

https://brainly.com/question/16151549.

The displacement of thoughts, feelings, fears, wishes, and conflicts from past relationships onto new relationships is called transference.

The time period of the mass attached to a spring that oscillates and completes 51 full cycles in 35 seconds is approximately 0.686 seconds, and the frequency is about 1.458 Hz.

To determine the time period (T) and frequency (f) of the oscillating mass attached to a spring, we can use the relationship between the number of cycles (n), total time (t), and the time period (T = t/n). If the mass completes 51 full cycles in 35 seconds, the time period (T) is calculated as:

In conclusion, the time period of the system is approximately 0.686 seconds, and the frequency is about 1.458 Hz.

Answer:

option B.

Explanation:

The correct answer is option B.

when the ball drops, the velocity of the ball before the collision is v

After the collision, the velocity of the ball is the same but in the opposite direction.

Impulse delivered to the ball and the floor, in this case, is not zero.

The magnitude of the momentum remains the same but the direction of the ball changes.

The true statement about the collision between the ball and the floor is that the ball's momentum is conserved.

The term momentum is physics is the product of mass and velocity. Momentum is a vector quantity hence when discussing momentum, we have to take the magnitude and direction into account.

The true statement about the collision between the ball and the floor is that the ball's momentum is conserved.

Learn more about momentum: https://brainly.com/question/904448

Final answer:

To find the displacement, subtract the distance traveled in one direction from the distance traveled in the opposite direction.

Explanation:

To solve this problem, we need to consider the concept of displacement. Displacement is a vector quantity that represents the change in position of an object. To find the displacement, we can subtract the distance traveled in one direction from the distance traveled in the opposite direction. In this case, the girl rides 5.4 km due east and then turns around and rides back to her starting point. So her displacement is 5.4 km - 5.4 km = 0 km.

Answer:

Average speed: 0.1 km/min

Explanation:

The average speed of a body is the ratio between the total distance covered and the time taken:

[tex]v=\frac{d}{t}[/tex]

where

d = distance covered

t = time taken

In this problem, we have:

- Distance covered is the sum of the two distances:

d = 6.0 + 1.0 = 7.0 km

- Time taken is the sume of the two times:

t = 54 + 16 = 70 min

Therefore, the average speed is

[tex]v=\frac{7.0}{70}=0.1 km/min[/tex]

Nathan drops marbles down two ramps that have different lengths. It takes the marbles 10 seconds to reach the bottom of both ramps.Which statement is TRUE?

answer choices

Marble 1 has a faster speed than Marble 2.

Marble 2 has a faster speed than Marble 1.

Both the marbles travel at the same speed.

There is not enough data to compare the speeds of marbles.

Marble 2 has a faster speed than Marble 1.

Option B.

The speed is defined as the distance covered per unit time. Here in the question, 2 balls cover equal distances in same time.

Time taken by the ball = 10 seconds.

Distance covered by 1st ball = 20 cm.

Distance covered by 2nd ball = 3cm.

So speed of the 1st ball = 2cm/sec.

Speed of the 2nd ball = 3 cm /sec.

So,it's very much evident that speed of 2nd Marble is much higher than the speed of the 1st marble.

Answer:

Explanation:

a) The magnitude of the net force on the student = 0 N since the student is standing still on level ground and upward reaction force = downward force.

b) the magnitude of the contact force on the student by the backpack = 80 N since the student was backing the backpack

c) the magnitude of the contact force o the student by the ground = 550 N + 80 N = 630 N reactional force on the student

Answer:

Computer A is 1.41 times faster than the Computer B

Explanation:

Assume that number of instruction in the program is 1

Clock time  of computer A is [tex]CT_{A} =200 ps[/tex]

Clock time  of computer B is [tex]CT_{B} =250 ps[/tex]

Effective CPI of computer A is [tex]CPI_{A} =1.5[/tex]

Effective CPI of computer B is[tex]CPI_{B} =1.7[/tex]

CPU time of A is

[tex]CPU_{time}=instructions \times CPA_{A} \times CT_{A}\\CPU_{time}=1 \times 1.5 \times 200=300 sec[/tex]

CPU time of B is

[tex]CPU_{time}=instructions \times CPA_{B} \times CT_{B}\\CPU_{time}=1 \times 1.7 \times 250=425 sec[/tex]

Hence Computer A is Faster by [tex]\frac{425}{300} =1.41[/tex]

Computer A is 1.41 times faster than the Computer B

Answer:

As magnification increases, the area of the field of view increases, the depth of the field of view decreases, the working distance decreases, and the amount of light required increases.

As magnification increases, the area of the field of view decreases, the depth of the field of view decreases, the working distance decreases, and the amount of light required increases.

Area of the field of vision: As magnification is increased, the field of view narrows, and you can see less of the object or scene that you are watching. The area you can see reduces as a result of the field of view is smaller.

Depth of field: The range of distances inside an object or scene that simultaneously seem in focus is referred to as depth of field. The depth of field tends to get shallower as magnification gets bigger. This makes it more difficult to simultaneously examine objects at various depths because only a limited range of distances will ever be in focus.

The working distance is the separation between the thing being observed and the objective lens (or magnifying device). The working distance often reduces as magnification rises. To keep the object in focus, you must move it closer to the lens or microscope.

Higher magnification frequently necessitates additional light in order to preserve image quality and visibility. The features become more noticeable when you zoom in on a smaller region, although they might need more light to be clearly visible. At greater magnifications, insufficient light can produce a hazy or dim image, therefore more light would be required.

Hence, As magnification increases, the area of the field of view decreases, the depth of the field of view decreases, the working distance decreases, and the amount of light required increases.

To learn more about Magnification, here:

https://brainly.com/question/28957672

#SPJ6

Answer:

If there were no greenhouse effect, liquid water would not exist on the surface of the Earth.

The Earth has reached thermal equilibrium, emitting the same amount of energy into space as it absorbs from the Sun.

The more carbon dioxide there is in an atmosphere, the stronger the greenhouse effect will be.

Explanation:

Without greenhouse gases like carbon dioxide, the entire Earth would be well below the freezing temperature of water. These gases slow the radiation of infrared light into space, warming the planet until it reaches thermal equilibrium.

The greenhouse effect is a natural phenomenon that plays a major role in the Earth's climate. It involves the trapping of heat by greenhouse gases in the atmosphere, which raises the Earth's surface temperature. Without the greenhouse effect, the Earth would be much colder.

The greenhouse effect is a natural phenomenon that plays a major role in the Earth's climate. It is similar to the heating of a greenhouse or a car left in the sun with the windows rolled up. The greenhouse gases in the atmosphere, such as carbon dioxide and methane, trap heat from the sun, preventing it from escaping back into space. Without the greenhouse effect, the Earth's average surface temperature would be well below freezing and Earth would be locked in a global ice age.

Greenhouse gases like carbon dioxide and water vapor absorb and emit radiation, which is an important factor in the greenhouse effect. Approximately half of the radiation from the sun passes through these gases in the atmosphere and strikes the Earth. This radiation is converted into thermal radiation on the Earth's surface, which is then partially reflected back to the Earth's surface by greenhouse gases. The more greenhouse gases there are in the atmosphere, the more thermal energy is reflected back to the Earth's surface, causing it to heat up.

The greenhouse effect is responsible for raising the Earth's surface temperature by about 23 °C. Changes in global climate due to the greenhouse effect can lead to more intense storms, changes in precipitation patterns, reduction in biodiversity, and rising sea levels.

https://brainly.com/question/1577730

#SPJ3

Answer:106.6N

Explanation:

Centripetal force is a force that cause a body to move along a circular path in a field. The body possesses a mass and velocity(since it's moving) and also radius alone the circular path on which it moves.

Given mass (m) = 2kg, velocity (v) = 8m/s and radius (r) = 1.2m

Centripetal acceleration(a)= v²/r

Centripetal force = ma = mv²/r

Substituting this values in the formula above we have;

Centripetal force = 2×8²/1.2m

Centripetal acceleration = 128/1.2

= 106.6N

Answer:

b) twice the energy of each photon of the red light.

Explanation:

[tex]\lambda[/tex] = Wavelength

h = Planck's constant = [tex]6.626\times 10^{-34}\ m^2kg/s[/tex]

c = Speed of light = [tex]3\times 10^8\ m/s[/tex]

Energy of a photon is given by

[tex]E=h\nu\\\Rightarrow E=h\dfrac{c}{\lambda}[/tex]

Let [tex]\lambda_1[/tex] = 700 nm

[tex]\lambda_2=350\\\Rightarrow \lambda_2=\dfrac{\lambda_1}{2}[/tex]

For red light

[tex]E_1=\dfrac{hc}{\lambda_1}[/tex]

For UV light

[tex]E_2=\dfrac{hc}{\dfrac{\lambda_1}{2}}[/tex]

Dividing the equations

[tex]\dfrac{E_1}{E_2}=\dfrac{\dfrac{hc}{\lambda_1}}{\dfrac{hc}{\dfrac{\lambda_1}{2}}}\\\Rightarrow \dfrac{E_1}{E_2}=\dfrac{1}{2}\\\Rightarrow E_2=2E_1[/tex]

Hence, the answer is  b) twice the energy of each photon of the red light.

Answer:

b) twice the energy of each photon of the red light.

Explanation:

Given:

wavelength of red light, [tex]\lambda_r=7\times 10^{-7}\ m[/tex]

wavelength of ultraviolet light, [tex]\lambda_{uv}=3.5\times 10^{-7}\ m[/tex]

We know that the energy of a photon is given as:

[tex]E=h.\nu[/tex] ..............(1)

where:

h = plank's constant [tex]=6.626\times 10^{-34}\ J.s[/tex]

[tex]\nu=[/tex]  frequency of the wave

we have the relation:

[tex]\nu=\frac{c}{\lambda}[/tex] ...................(2)

From (1) and (2) we have:

[tex]E=\frac{h.c}{\lambda}[/tex]

Energy of photons for ultraviolet light:

[tex]E_{uv}=\frac{6.626\times 10^{-34}\times 3\times 10^8}{3.5\times 10^{-7}}[/tex]

[tex]E_{uv}=5.6794\times 10^{-19}\ J[/tex]

Since the energy of photons is inversely proportional to the wavelength of the light hence the photon-energy of ultraviolet light is double of the photon-energy of the red light as the wavelength of the red light is twice to that of ultraviolet light.

Answer:

An unbalanced force is defined as a force that is not canceled out by one or more other forces acting in other directions.

Explanation:

According to Newton's first law of motion,  “An object in a constant state of motion remains in that constant state of motion unless acted upon by an unbalanced force.” An unbalanced force is a force that changes the speed, position, or direction of an object. It is not canceled out by other forces acting in other directions.

An unbalanced force is defined as a force that is not canceled out by other forces acting in different directions. This results in a net force that causes an object to accelerate, changing its state of motion.

An unbalanced force is defined as a force that is not canceled out by other forces acting in different directions. allows an object to remain at rest cause an object to accelerate in a direction opposite to the unbalanced force is not canceled out by one or more other forces acting in other directions allows an object to move at constant speed.

When forces on an object are unbalanced, it means that the net force acting on the object is not zero, leading to a change in the object's motion. This unbalanced force results in acceleration according to Newton's second law of motion, which states that [tex]\( F = ma \)[/tex] force equals mass times acceleration.

Answer:

Explanation:when a tape is moved past a small coil of wire due to a non uniform field,the voltage is induced in the coil. A practical example of this is a tape recorder in which a moving tape produces sound energy..

Answer:

While the Applied Force (force exerted) is decreasing, the velocity is decreasing

Explanation:

From Newton's second law of motion, which states that the rate of change of linear momentum is directly proportional to the applied force, and takes place in the direction of the applied force.

Momentum (P) = MV

Thus, F ∝ MV/t

where;

F is the applied force

M is the mass of the object

V is the velocity of the object

From the equation above, force is directly proportional to the velocity of the refrigerator (F∝V). That is, as the applied force is decreasing, the velocity is decreasing and vice versa.

Therefore, while the Applied Force (force exerted) is decreasing, the velocity is decreasing.

Answer:

on mastering physics its b.increasing

Explanation:

Answer:

The magnitude of the displacement is 127.43m and the direction is 38°North of East

Explanation:

Final answer:

To find the magnitude and direction of the fourth displacement in a cave survey, vector components can be used. By breaking down the given displacements into their north and east components, calculating the net displacements, and using the Pythagorean theorem and trigonometry, the magnitude and direction of the fourth displacement can be determined.

Explanation:

To find the magnitude and direction of the fourth displacement, we can use vector components. First, let's break down the given displacements into their north and east components:

Displacement 1: 190 m west (0 north, -190 east)

Displacement 2: 220 m at 45.0° east of south (-220 sin(45°) north, 220 cos(45°) east)

Displacement 3: 270 m at 30.0° east of north (270 sin(30°) north, 270 cos(30°) east)

Next, we can add up the north and east components separately to find the net north and east displacements. Lastly, we can use these net displacements to calculate the magnitude and direction of the fourth displacement using the Pythagorean theorem and trigonometry.

Answer:

B. When the racket hits the tennis ball with a force, the tennis ball applies an equal but opposite force to the racket

Explanation:

Newton's third law of motion states that for every action there is an equal and opposite reaction. Therefore, when Krista's racket hits the tennis ball with a force, the tennis ball applies an equal but opposite force to the racket.

When the racket hits the tennis ball with a force, the tennis ball applies an equal but opposite force to the racket. Therefore option B is correct.

According to Newton's third law of motion, for every action, there is an equal and opposite reaction.

In this scenario, when Krista hits the tennis ball with her racket (the action), the tennis ball exerts an equal but opposite force back onto the racket (the reaction).

This is depicted by option B, which correctly states that the tennis ball applies an equal but opposite force to the racket. This law underscores the idea that forces always come in pairs, and the forces are exerted on two different objects.

The force Krista applies to the ball is met with an equal force from the ball back onto her racket, causing the ball to fly in the opposite direction.

Therefore option B is correct.

Know more about Newton's law:

https://brainly.com/question/34706880

#SPJ3

Answer:

78.4 m

Explanation:

Using newton's equation of motion,

S = ut + 1/2gt²......................... Equation 1

Where S = Height, t = time, u = initial velocity, g = acceleration due to gravity.

Note: Taking upward to be negative, and down ward positive

Given: u = 49 m/s, t = 2.0 s, g = -9.8 m/s²

Substitute into equation 1

S = 49(2) - 1/2(9.8)(2)²

S = 98 - 19.6

S = 78.4 m

Hence the height of the ball two seconds later = 78.4 m

Answer:

54.67 N

Explanation:

The total energy produced is the product of power and time duration:

E = Pt = 82 * 1 = 82 J

Which is converted from work, product of forced extended over a displacement

W = E = Fs = F*1.5 = 82

F = 82 / 1.5 = 54.67 N

So the magnitude of the force exerting on the handle is 54.67 N

Answer: Option (b) is the correct answer.

Explanation:

Heat is defined as the energy obtained by the molecules of an object that travels from a hotter body to a colder body.

For example, a metal spoon placed in a cup full of hot tea. Then transfer of heat will take place from the tea to the spoon.

And, this transfer of heat will continue till the temperature of both the objects become equal.

Thus, we can conclude that heat is the energy that moves from a hotter object to a colder object.

Answer:

0.0016 cm

Explanation:

[tex]\alpha_b[/tex] = Thermal coefficient of expansion of brass = [tex]19\times 10^{-6}\ /^{\circ}C[/tex]

[tex]\alpha_g[/tex] = Thermal coefficient of expansion of glass = [tex]9\times 10^{-6}\ /^{\circ}C[/tex]

[tex]\Delta T[/tex] = Change in temperature = [tex](60-20)^{\circ}C[/tex]

[tex]R_0[/tex] = Initial radius = 4 cm

Change in radius of material is given by

[tex]R=R_0(1+\alpha\Delta T)[/tex]

Difference in radii of the lid and jar

[tex]\Delta R=R_b-R_g\\\Rightarrow \Delta R=R_0(1+\alpha_b\Delta T)-R_0(1+\alpha_g\Delta T)\\\Rightarrow \Delta R=R_0(\alpha_b-\alpha_g)\Delta T\\\Rightarrow \Delta R=4\times (19\times 10^{-6}-9\times 10^{-6})\times (60-20)\\\Rightarrow \Delta R=0.0016\ cm[/tex]

The size of the gap is 0.0016 cm or 0.000016 m

Final answer:

Heating the brass lid and glass jar causes the lid to expand more than the jar, creating a gap between them. To find the size of the gap, we can calculate the change in radius of the lid. Using the given information, we can find that the size of the gap is approximately 19.2 x [tex]10^-^3[/tex] cm.

Explanation:

When the brass lid and glass jar are heated in hot water, their temperatures increase. The lid, being made of metal, expands more than the glass jar due to the higher coefficient of expansion for metals. This causes the lid to loosen its grip on the jar, creating a gap between them.

To find the size of the gap, we need to calculate the difference in radius of the lid before and after heating. The inside diameter of the lid is given as 8.0 cm at 20 degrees C. We can calculate the radius using the formula r = ½ d, where d is the diameter. The radius at 20 degrees C is therefore 4.0 cm.

Now, let's calculate the radius at 60 degrees C. To do this, we need to know the coefficient of linear expansion for brass. Assuming it is 19x10^-6 /°C, we can use the formula: ∇r = αr0∇T, where ∇r is the change in radius, α is the coefficient of linear expansion, r0 is the initial radius at a reference temperature, and ∇T is the change in temperature. Plugging in the values, we get: ∇r = (19x[tex]10^-^6[/tex] /°C) x (4.0 cm) x (60 °C - 20 °C) = 19.2 x [tex]10^-^3[/tex] cm.

Therefore, the size of the gap that develops by heating the lid and jar is approximately 19.2 x [tex]10^-^3[/tex] cm.

Answer:

Fraction of the nickel atoms removed = 1.02 x 10 raised to power -11

Explanation:

The detailed and step by step derivation with appropriate substitution is as shown in the attached files.

To calculate the fraction of nickel atoms' electrons needed to support the weight of a nickel coin when placed 1 meter above it, we use the weight of the coin and Coulomb's law to determine the necessary charge. This charge divided by the elementary charge gives us the number of electrons needed, providing the fraction when compared to the total number of electrons in the coin.

To calculate what fraction of a nickel coin's electrons would need to be removed and placed 1.00 m above it to support its weight, we should use the concept of electrostatic force. We'll begin by determining the weight of the coin in newtons (since weight is a force). Next, we will determine the number of moles of nickel in the coin using its atomic mass, and from that, calculate the number of nickel atoms. With the atomic structure of nickel, we find the total number of electrons in the coin. Using Coulomb's Law, we can equate the electrostatic force due to the separated charges to the weight of the coin to solve for the fraction of electrons needed.

First, we need to convert the mass of the coin into weight using the formula weight (W) = mass (m) * gravity (g). Since the coin has a mass of 5.00 g (which is 0.005 kg) and the gravitational constant is approximately 9.8 m/s², the weight W is 0.049 N. Next, we use the atomic mass of nickel (58.7 u) to find the number of moles in 5.00 g of nickel. This number is given by the mass of the coin divided by the atomic mass of nickel. The number of atoms is the number of moles times Avogadro's number (approximately 6.022 × 10²³ atoms/mole).

Therefore, the total number of electrons in the 5.00 g of nickel is the number of atoms times the number of electrons per atom, which for nickel is 28. To support the coin at a distance of 1.00 m, the electrostatic force (Felectrostatic) should be equal to the weight of the coin, or 0.049 N. Using Coulomb's law, Felectrostatic = k * |q₁ * q₂| / r², where k is Coulomb's constant (approximately 8.988 × 10⁹ N·m²/C²), q₁ and q₂ represent the charges, and r is 1.00 m in our case. By solving this equation for q (assuming both q₁ and q₂ would be the same since it's the same electrons that have been separated), we can find the necessary charge to create a force equal to the weight of the coin.

After finding this charge, we divide by the elementary charge (approximately 1.602 × 10⁻¹⁹ C) to get the number of electrons needed. Dividing this number by the total number of electrons in the coin gives us the fraction of the nickel atoms' electrons needed to support the weight of the coin.

Answer:

4 conditions

Explanation:

The National Electrical Code (NEC) provides safety guidelines for the installation of electrical wiring and electrical equipment in the United States. The purpose behind NEC is to standardize the safe electrical installation practices.

There is always a confusion among people to distinguish between inside or outside of a building or structure. Therefore, NEC has listed 4 conditions in the Article 230.6 where it has mentioned conductors to be considered outside a building or structure.

Conductors are considered outside a building when they are installed:

1. Under not less than 2 inches of concrete beneath a building or structure.

2. Within a building or structure in a raceway that is encased in no less than 2 inches thick of concrete or brick.

3. Installed in a vault that meets the construction requirements of Article 450, Part III.

4. In conduit under not less than 18 inches of earth beneath a building or structure.

Answer:

[tex]v_y=-1.2m/s,a_y=-0.76m/s^2[/tex]

Explanation:

We are given that

[tex]y=(0.05x^2)[/tex]

Where x (in m)

x component of velocity, [tex]v_x=-4m/s[/tex]

x- component of acceleration,[tex]a_x=-1.2 m/s^2[/tex]

x=3 m

We have to find the y-component of velocity and acceleration at this instant.

Differentiate w.r.t. time

[tex]\frac{dy}{dt}=0.05\times 2x\frac{dx}{dt}[/tex]

[tex]\frac{dy}{dt}=0.1x\frac{dx}{dt}=0.1xv_x[/tex]

By using the formula

[tex]\frac{dx^n}{dx}=nx^{n-1}[/tex]

[tex]v_x=\frac{dx}{dt}[/tex]

Substitute the values

[tex]v_y=\frac{dy}{dt}=0.1(3)\times (-4)=-1.2m/s[/tex]

Again differentiate w.r.t. t

[tex]a_y=\frac{dv_y}{dt}=0.1v_x+0.1x\frac{d(v_x)}{dt}[/tex]

Substitute the values

[tex]a_y=0.1(-4)+0.1(3)(-1.2)=-0.4-0.36=-0.76m/s^2[/tex]

Where [tex]a_x=\frac{dv_x}{dt}[/tex]

Hence, the y- component of velocity and acceleration

[tex]v_y=-1.2m/s,a_y=-0.76m/s^2[/tex]

To find the y components of velocity and acceleration, differentiate the equation y = 0.05x^2 with respect to time. Plug in the given values to find vy and ay at x = 3m.

To find the corresponding y components of velocity and acceleration at x = 3m, we need to differentiate the equation y = 0.05x^2 with respect to time. Differentiating y with respect to time gives vy = dy/dt = d/dt(0.05x^2) = 0.1x(dx/dt). Plugging in the given values dx/dt = -4m/s and x = 3m, we can find vy. Similarly, to find the y-component of acceleration, we differentiate vy with respect to time, which gives ay = dvy/dt = d/dt(0.1x(dx/dt)) = 0.1(dx/dt)(dx/dt) + 0.1x(d^2x/dt^2). Plugging in the given values dx/dt = -4m/s and d^2x/dt^2 = -1.2m/s^2, we can find ay.

https://brainly.com/question/32563162

#SPJ3

Answer:

a) Average velocity = 156.7m/s

b) Speed of blast wave is 0.457 times the speed of sound wave

Explanation:

The step by step calculations is as shown in the attached file.

Answer:

Velocity,c = 156.67m/s

Explanation:  Altitude, d = 23.5km or 23500m

Time duration, T = 2 minutes + 30 seconds = (120 + 30) seconds = 150 seconds

a) Frequency, F = 1/T= 1/150 Hz

Hence, Velocity, c = d X F = 23500 X 1/150

∴ c = 156.67 m/s

b)  The speed of sound increases as the wave moves from a lighter medium to denser medium. While the of the superbolide meteor decreases from a lighter medium to denser medium.

The weight of the book is calculated using the formula for weight, which is the mass of the object times the acceleration due to gravity. Given the mass of the book and the standard acceleration due to gravity, the weight of the book is 12.74 Newton.

To calculate the weight of the book, we need to remember from our physics knowledge that weight is the force exerted by an object under the influence of gravity. The formula for weight (W) is W = m*g, where m is the mass of the object, and g is the acceleration due to gravity. In most parts of the Earth, the acceleration due to gravity is approximately 9.8 m/s^2.

So in this case, the weight of the book is calculated as follows: W = 1.3 kg * 9.8 m/s^2 = 12.74 N. Therefore, the weight of the book is 12.74 Newton. Note that the coefficient of static friction is not needed to calculate the weight of the book.

https://brainly.com/question/31409659

#SPJ3

The weight of a book with a mass of 1.3 kg is calculated using the formula W = m x g, resulting in 12.74 N.

The weight of the book in Newtons can be calculated using the formula for weight, which is the mass of the object (m) multiplied by the acceleration due to gravity (g). The acceleration due to gravity is approximately 9.80 m/s² on Earth. Therefore, to find the weight (W) of the book, you use the equation W = m  imes g.

For a book with a mass of 1.3 kg, the calculation is W = 1.3 kg times 9.80 m/s² = 12.74 N.

This is the weight of the book that the woman must counteract with the normal force exerted by her hands, which is equal in magnitude to the weight of the book but in the opposite direction, as explained by Newton's third law of motion.

Answer:

[tex]s=5.79\ km[/tex]

[tex]\theta=47^{\circ}[/tex] east of south

Explanation:

Given:

Now refer the schematic for visualization of situation:

[tex]y=d'.\sin47^{\circ}-d[/tex]

[tex]y=8.4\times \sin47-5.3[/tex] ...............(1)

[tex]x=d'.\cos47^{\circ}[/tex]

[tex]x=8.4\times \cos47^{\circ}[/tex] .................(2)

Now the direction of the desired position with respect to south:

[tex]\tan\theta=\frac{y}{x}[/tex]

[tex]\tan\theta=\frac{8.4\times \sin47}{8.4\times \cos47}[/tex]

[tex]\theta=47^{\circ}[/tex] east of south

Now the distance from the current position to the desired position:

[tex]s=\sqrt{x^2+y^2}[/tex]

[tex]s=\sqrt{(8.4\times \cos47)^2+(8.4\times \sin47-5.3)^2}[/tex]

[tex]s=5.79\ km[/tex]

Answer:

4.15 m/s

Explanation:

As the total energy must be conserved (neglecting air resistance) the change in gravitational potential energy, must be equal to the change in kinetic energy:

ΔE = ΔK + ΔU =0

If we take as a zero reference level for the gravitational potential energy, the height of the swing seat above the ground, (which is equal to 0.21 m), we can find the initial gravitational energy, considering the height of the point where the seat is released, regarding this point:

h₀ = 1.09 m -0.21 m = 0.88 m

⇒ U₀ = m*g*h₀ = 400 N*0.88 m = 352 J

As Uf = 0, ΔU = Uf -U₀ = -352 J

As the swing starts from rest, K₀=0, so we can say:

ΔK = Kf = [tex]\frac{1}{2} *m*vf^{2}[/tex]  (1)

As ΔK = -ΔU ⇒ ΔK = 352 J (2)

From (1) and (2) we can solve for vf, as follows:

[tex]vf = \sqrt{\frac{2*352J}{40.8kg}} = 4.15 m/s[/tex]

So, when the swing passes through its lowest position, Betty moves at 4.15 m/s.

Final answer:

Betty is moving at a speed of approximately 2.86 m/s when the swing passes through its lowest position.

Explanation:

To calculate the speed at the lowest position of Betty on the swing, we can use the principle of conservation of mechanical energy. At the highest point, all of Betty's potential energy is converted into kinetic energy. So we can write:

Initial potential energy = Final kinetic energy

mgh = 0.5mv^2

where m is the mass of Betty, g is the acceleration due to gravity, h is the initial height, and v is the velocity at the lowest point.

Plugging in the values, we get:

(400 N)(0.21 m) = 0.5(400 N)v^2

After simplifying and solving for v, the velocity at the lowest point is approximately 2.86 m/s.