After takeoff, an airplane climbs at an angle of 30° at a speed of 215 ft/sec. How long does it take for the airplane to reach an altitude of 13,000 ft? (Round your answer to one decimal place.)

Answer and Explanation

It was initially specified that the receptacle outlet to be located within 50 ft of the electrical service equipment.

As well, instead of the receptacle being required within 50 ft., it is now required within 25 ft. of the service. This was to accommodate the typical 25 ft. cord used by many service electricians.

The rules apply to indoor service locations other than one-and two-family dwellings. For these locations, at least one 125-volt, single-phase, 15- or 20-ampere receptacle outlet must be installed in an accessible location within 25 ft. of the indoor electrical service equipment. The receptacle must be within the same room or area as the actual service equipment.

Having a maintenance receptacle near the electrical service allows for testing, servicing and connection of portable electrical data acquisition equipment for analyzing the electrical system.

Answer:

Explanation:

Potential Energy of an object is a function of elevation from datum thus assuming datum to be ground, the potential energy of the person increases as he moves up to the top.

When a person is skating from the top of the track to the bottom then his potential energy is getting converted into the kinetic energy so his kinetic energy increases as he moves down.

When a person is moving from top to bottom his kinetic energy increases which is a function of mass and velocity. As mass is fixed therefore his velocity increases as he moves down

Final answer:

When the person is skating from the bottom of the track back up to the top, potential energy increases. When the person is skating from the top of the track down to the bottom, kinetic energy increases. When the person is skating from the top of the track down to the bottom, velocity increases.

Explanation:

When the person is skating from the bottom of the track back up to the top, her potential energy increases. When the person is skating from the top of the track down to the bottom, his kinetic energy increases. When the person is skating from the top of the track down to the bottom, her velocity increases.

Answer: D) occurs when water is evaporated.

Explanation:

A physical change is defined as a change in which there is alteration in shape, size etc. No new substance gets formed in these reactions.

A chemical change is defined as a change in which a change in chemical composition takes place. A new substance is formed in these reactions.

a).  iron rusts :the chemical reaction occurs by combination of iron with oxygen , thus a chemical change.

b) sugar is heated into caramel. the chemical reaction occurs by decomposition , thus a chemical change.

c) glucose is converted into energy within your cells: the chemical reaction occurs by decomposition , thus a chemical change.

d) when water is evaporated : Only the state changes and thus a physical change and cannot be reversed.

e) when propane is burned for heat: the chemical reaction as propane combines with oxygen to form carbon dioxide and water , thus a chemical change.

Answer:

[tex]F'=2F[/tex]

Explanation:

According to Coulomb's law and assuming the objects as point charges, the magnitude of the electric force that each object exerts on the other is defined as:

[tex]F=\frac{kq_Aq_B}{d^2}[/tex]

Here k is thee Coulomb constant, [tex]q_A[/tex] and [tex]q_B[/tex] are the charges of the objects and d is the distance of separation between them. We have [tex]q'_A=2q_A[/tex]:

[tex]F'=\frac{kq'_Aq_B}{d^2}\\F'=\frac{k2q_Aq_B}{d^2}\\F'=2\frac{kq_Aq_B}{d^2}\\F'=2F[/tex]

Answer and Explanation

The concept of parallax and relative motion is responsible for this.

That is, the photographer's motion prompts her to see parallax for the man and the trees, because their positions appear to keep shifting even though they are not really moving.

The apparent movement of the man and trees relative to distant mountains as the photographer moves is a result of a physics concept called parallax. Parallax causes nearer objects to appear to move more than farther ones as the observer's position changes.

The phenomenon you're describing occurred as a result of a concept in physics known as parallax. Parallax refers to the apparent movement of objects when the observer's position changes. So in this case, as the photographer moves, the position of the man and the trees appear to change relative to the distant mountains. This is because nearer objects appear to move more than farther objects as the observer moves. So, the man and trees (which are closer) seem to shift their positions more than the mountains (which are farther away).

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Answer:

Bulbs in series will be dim

Explanation:

The voltage remain constant in a series circuit, thus bulbs in series circuit will get equally distributed voltage which is not equal to the voltage across the circuit or the voltage supplied

In case of parallel circuit, the voltage across the bulb is the same as the voltage across the circuit due to which bulbs will be brighter in case of parallel circuit

Answer:

[tex] m_i =\frac{1736.702 cal}{129 cal/gr}=13.46 gr[/tex]

So we need to add 13.46 gr of ice in order to reach the final equilibrium temperature of 49 C

Explanation:

For this case we need to use the fact that the sum for all the heats involved in the system are 0, since we assume an equilibrium state.

Data given

[tex]m_p = 303 gr[/tex] mass of the porcelain cup

[tex] cp_p = 0.260 cal/g C[/tex] the specific heat for the porcelain cup

[tex] T_{ip} = T_{ic}= 71 C[/tex] initial temperature for the coffee and the porcelain cup.

[tex] V_{c}= 161 cm^3[/tex] Volume of the coffee.

We can convert this to m^3 and we got 0.000161m^3 and assuming the density fot the coffee equal to the water 1 Kg/m^3 the mass would be:

[tex] m_c = 1 kg/m^3 *0.000161 m^3 = 0.000161 kg=0.161 Kg[/tex]

[tex] Cp_{c} = 1 cal/g C[/tex] Specific heat for the coffee

[tex] m_i =?[/tex] mass of ice required

[tex] T_e= 49C[/tex] equilibrium temperature

[tex]L_f = 80 cal/g [/tex] represent the latent heat of fusin since the ice change the state to liquid.

Solution to the problem

Using this formula:

[tex] \sum_{i=1}^n Q_i = 0[/tex]

We have this:

[tex] m_p cp_p (T_e -T_{ip}) + m_{c} cp_c (T_e -T_{ic}) +m_i L_f + m_i cp_w (T_e -0) =0[/tex]

Now we can replace and we have this:

[tex] 303 gr *(0.260 cal/g C) (49-71)C + 0.161 gr*(1 cal/g C)(49-71)C +m_i [80 cal/gr+(1cal/g C)(49-0)C]=0[/tex]

And now we can solve for [tex] m_i[/tex] and we have:

[tex]-1733.16cal -3.542cal +m_i [129 cal/g]=0[/tex]

[tex]m_i =\frac{1736.702 cal}{129 cal/gr}=13.46 gr[/tex]

So we need to add 13.46 gr of ice in order to reach the final equilibrium temperature of 49 C

Answer:

- 1.33m/s

Explanation:

We choose the system to be the child and the sled. The surface is friction less, which means that there are no forces exerted on the system horizontally. This means that the horizontal momentum component of the system is constant and conserved.

So we can use the conservation momentum principle to find the velocity of the child just after he leaves the sled.

This is shown in the attached file.

The child’s velocity in the horizontal direction relative to the ground at the instant she left the sled is 1.33 m/s.

It should be noted that velocity simply means the directional speed of an object in motion.

In this case, the velocity will be:

= ((30 + 10) × 6) - (10 × 20)/30

= (40 × 6) - (200)/30

= (240 - 200)/30

= 40/30

= 1.33 m/s

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Incomplete question as the car's  speed is missing.I have assumed car's  speed as 6.0m/s.The complete question is here

An amusement park ride consists of a car moving in a vertical circle on the end of a rigid boom of negligible mass. The combined weight of the car and riders is 6.00 kN, and the radius of the circle is 15.0 m. At the top of the circle, (a) what is the force FB on the car from the boom (using the minus sign for downward direction) if the car's speed is v 6.0m/s

Answer:

[tex]F_{B}=-5755N[/tex]

Explanation:

Set up force equation

∑F=ma

∑F=W+FB

[tex]\frac{mv^{2} }{R}=W+F_{B}\\ F_{B}=\frac{mv^{2} }{R}-W\\F_{B}=\frac{(W/g)v^{2} }{R}-W\\F_{B}=\frac{(6000N/9.8m/s^{2} )(6m/s)^{2} }{(15m)}-6000N\\F_{B}=-5755N[/tex]

The minus sign for downward direction

Answer:

x -component of dog's velocity = 8.265m/s

y- component of dog's velocity = 1.389m/s

Explanation:

The detailed and step by step calculation is as shown in the attached file.

Answer: The net flux of carbon into the atmosphere without including the contribution from burning fossil fuels is positive.

Explanation:

The human activity of burning fossil fuels inevitably contributes to the increase in carbon dioxide and other gases in the Earth's atmosphere. As a result of this occurrence, a natural greenhouse appears. The greenhouse effect is the process of warming the Earth's surface and the lower layers of the atmosphere, resulting from the leakage of heat radiation.

Answer:

C

Explanation:

earth science climate change unit test

Final answer:

To determine the speed of the raindrops relative to the ground and their angle, we analyze the observations of rain angle in two car speeds using trigonometry and the Pythagoras theorem, concluding with the application of the tangent function and arctan.

Explanation:

When driving north at 25 m/s, rain appears to make an angle of 38 degrees with the vertical due to the combination of the rain's vertical speed and the horizontal speed of the car. However, when driving south at the same speed, the rain appears to fall vertically, indicating the horizontal component of the rain's velocity is equal to the car's speed. To determine the speed of the raindrops relative to the ground and the angle of the raindrops relative to the ground, we can use trigonometry.

Given the observation that the rain appears vertical when driving south at 25 m/s, it implies the horizontal velocity of the rain is 25 m/s (equal but opposite to the car's velocity, thereby canceling it out). From the 38-degree angle observation, we can use tan(38 degrees) = vertical component / horizontal component to find the vertical speed. The answer is derived from tan(38 degrees) = vertical component / 25 m/s, which allows us to calculate the vertical component.

The speed of the raindrops relative to the ground is then found by calculating the resultant of the horizontal and vertical components using Pythagoras theorem, and the angle of the raindrops is found by taking the arctan of the vertical component over the horizontal component.

Answer:

The speed of Sam at the bottom is 7.19 m/s.

Explanation:

Given that,

Mass of Sam = 79 kg

Height = 11 m

Length = 120 m

Coefficient of kinetic friction = 0.07

Suppose, an object of mass m is at rest at the top of a smooth slope of height h and length L. The coefficient of kinetic friction between the object and the surface, micro-kilometer , is small enough that the object will slide down the slope if given a very small push to get it started.

We need to calculate the speed at the bottom

Using conservation of energy

[tex]P.E=K.E+\text{energy lost of friction}[/tex]

[tex]mgh=\dfrac{1}{2}mv^2+\mu mg(\sqrt{L^2-h^2})[/tex]

[tex]v^2=2gh-2\mu g(\sqrt{L^2-h^2}[/tex]

[tex]v=\sqrt{2gh-2\mu g(\sqrt{L^2-h^2}}[/tex]

Where, m = mass

h = height

L= length

v = speed

g = acceleration due to gravity

Put the value into the formula

[tex]v=\sqrt{2\times9.8\times11-2\times0.07\times9.8(\sqrt{120^2-11^2})}[/tex]

[tex]v=7.19\ m/s[/tex]

Hence, The speed of Sam at the bottom is 7.19 m/s.

Velocity is the rate of change of position. Sam's velocity at the bottom of the slope with a height of 11 m is 13.8844 m/s.

Velocity is the rate of change of position of an object with respect to time.

[tex]v = \dfrac{ds}{dt}[/tex]

We know that at the topmost height, the weight of Sam will act as potential energy, while during skiing down this potential energy will be partially converted to kinetic energy and part will be converted to heat or can say will be lost due to the friction, therefore,

Potential Energy = Kinetic energy + Energy loss due to the friction,

[tex]mgh = \frac{1}{2}mv^2 + \mu gh\sqrt{L^2+H^2}\\\\mgh - \mu gh\sqrt{L^2+H^2} = \frac{1}{2}mv^2\\\\2mgh - 2\mu gh\sqrt{L^2+H^2} = mv^2\\\\2gh(m - \mu \sqrt{L^2+H^2}) = mv^2\\\\v^2 = \dfrac{2gh}{m}(m - \mu \sqrt{L^2+H^2})[/tex]

Substitute the values,

Mass, m = 79 kg

Height, H = 11 m

Length, L = 120 m

Coefficient of kinetic friction, μ = 0.07

Acceleration due to gravity, g = 9.81 m/s²

[tex]v^2 = \dfrac{2 \times 9.81 \times 11}{79}[79-0.07\sqrt{120^2+11^2}]\\\\v^2 = 215.82 - 23.0442\\\\v = 13.8844\rm\ m/s[/tex]

Hence, Sam's velocity at the bottom of the slope with a height of 11 m is 13.8844 m/s.

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Answer:

travel = 1111.11 km or ( 691.66 miles ) north of the equator

Explanation:

given data

travel = 10° N latitude

circumference of the Earth = 40,000 kilometers

solution

when we start at equator and travel whole world and finally reach that same point

so we cover 40,000 km  and that is circumference of Earth

so that we cover = 360° latitude

and here distance travel in each degree of latitude will be

distance travel in each degree = [tex]\frac{40000}{360}[/tex]

distance travel in each degree = 111.11 km

so here for travel to 10 degrees N

so travel is = 111.11 ×  10 =

travel = 1111.11 km or ( 691.66 miles ) north of the equator

Answer

IF the earth's average surface temperature were to increase, the amount of radiation emitted from the earth's surface would _increase_ and the wavelength of peak emission would shift toward _shorter_ wavelengths.

Explanation:

The Energy of radiation emitted by the earth varies directly with the average surface temperature of the earth and inversely with the wavelength of emissions.

E = hv/λ

That is, E = k/λ

Therefore the most peak emissions (highest energies) would have shorter wavelengths.

Complete question:

if the earth's average surface temperature were to increase, the amount of radiation emitted from the earth's surface would __________ and the wavelength of peak emission would shift toward __________ wavelengths.

Answer:

if the earth's average surface temperature were to increase, the amount of radiation emitted from the earth's surface would Increase and the wavelength of peak emission would shift towards Shorter wavelengths.

Explanation:

Stefan-Boltzmann law, a fundamental law of physics, explains the relationship between an object's temperature and the amount of radiation that it emits. This law states that all objects with temperatures above absolute zero (0K) emit radiation at a rate proportional to the fourth power of their absolute temperature.

Expressed mathematically as; E = σT⁴

From this formula above, temperature is directly proportional to amount of radiation emitted.

Also, Energy of emitted radiation can be related to wavelength in the expression below

E =hc/λ

Where;

E is the energy of the emitted radiation

h is Planck's constant

c is the speed of light

λ is the wavelength of the emitted radiation

From the formula above, Energy of the emitted radiation is inversely proportional to the wavelength of the emitted rays.

The phasor currents for the load are 0.573 per unit. With the transformer phase shift, the generator supplies a voltage of 24.3 KV and 54.6 MW. Ignoring the transformer phase shift, the magnitudes remain the same, but the angles differ.

The complex power supplied to the load is P = 240 MVA * 0.9 = 216 MW and reactive power Q = 240 MVA * sqrt (1-0.9^2) = 106.3 MVAR. From this, you can compute the phasor currents IA, IB, and IC using the formula: I = S/V * conjugate of the power factor angle, giving IA = IB = IC = 0.573 per unit.

For b), taking leakage reactance into account, the generator voltage V = 1 + j0.11 * I, giving a voltage of 1.063 per unit. Because the generator is in Delta and the load is in Wye, there is a -30-degree shift in currents from the generator. So, IA, IB, and IC are 0.573 angle -30 degrees per unit.

For c), multiply the generator voltage by base voltage to determine the terminal voltage (1.063*23kV = 24.3 kV). The total real power supplied by the generator PG = VI*cos(theta) = 0.573*1.063*0.9 = 0.546 per unit, or 54.6 MW.

For d), if the transformer phase shift is ignored, we will still obtain the same magnitude of generator terminal voltage and real power, but the angles will be different, i.e., the currents will be in phase with the voltage, and not lagging by 30 degrees, because we didn't take into account the Y-D transformation.

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Answer: c. Both Technician A and Technician B.

Explanation:

In motor enginnering, in case of a clutch slippage. It can best be diagnosed by loading the engine while the clutch is released with the transmission in a high gear, such as fourth gear whilst releasing the clutch pedal slowly.

It's also true that a slipping clutch can cause friction surfaces warpage or hot spots.

This therefore makes both Technicians A and B right in their arguments.

Both Tech A, who suggests diagnosing clutch slippage by loading the engine in high gear, and Tech B, who states that a slipping clutch can lead to friction surface damage, are correct.

The subject of this question pertains to automotive technology, specifically the diagnosis of clutch issues in vehicles. When evaluating the statements given by the two technicians:

Tech A is correct in suggesting that clutch slippage can be diagnosed by loading the engine in a high gear while the clutch is released, as this can put enough load on the engine to reveal if the clutch is slipping.

Tech B is correct in saying that a slipping clutch can lead to warpage or the development of hot spots on the friction surfaces.

Therefore, the correct answer is c. Both Technician A and Technician B are correct in their assessments of clutch slippage diagnosis and potential consequences.

Answer:

Technician B is correct.

Explanation:

The given value of resistor having 3% tolerance means that the given quantity of the physical parameter can vary by 3% of what is specified. This variation can be either more or less than the quantified value.

The dimensions of the rectangular certificate with a perimeter of 32 inches and an area of 63 square inches can be 7 inches by 9 inches or 9 inches by 7 inches.

The subject of this question is Mathematics, specifically an application of algebra to solve for the dimensions of a rectangle when given its perimeter and area. Let’s denote length as L and width as W. The formulas for area and perimeter of a rectangle are given by Area = L * W and Perimeter = 2 * (L + W), respectively. Given that the area is 63 square inches and the perimeter is 32 inches, we can set up two equations.

From the perimeter, we have 2L + 2W = 32, simplifying gives us L = 16 - W.

We can then substitute this into the area equation, so (16 - W) * W = 63.

This simplifies and solved that gives us W = 7 or W = 9.

To find L, we substitute W = 7 / W = 9 into L = 16 - W. We get the pairs (L, W) as (9, 7) or (7, 9).

So the dimensions of the certificate can be 7 inches by 9 inches or 9 inches by 7 inches.

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Answer:

2670.90667586 J

108.573324964 dB

Explanation:

r = Distance = 120 m

A = Area = [tex]4\pi r^2[/tex]

I = Intensity of sound = [tex]7.2\times 10^{-2}\ W/m^2[/tex]

t = Time taken = 0.205 s

[tex]I_0[/tex] = Threshold intensity = [tex]10^{-12}\ W/m^2[/tex]

Power is given by

[tex]P=IA\\\Rightarrow E=7.2\times 10^{-2}\times 4\pi 120^2[/tex]

Energy is given by

[tex]E=Pt\\\Rightarrow E=7.2\times 10^{-2}\times 4\pi 120^2\times 0.205\\\Rightarrow E=2670.90667586\ J[/tex]

The total amount of energy is 2670.90667586 J

Sound intensity level is given by

[tex]\beta=10log\dfrac{I}{I_0}\\\Rightarrow \beta=10log\dfrac{7.2\times 10^{-2}}{10^{-12}}\\\Rightarrow \beta=108.573324964\ dB[/tex]

The sound level is 108.573324964 dB

The total amount of energy transferred away from the explosion by sound is 1.476 x 10^-2 Joules. The sound level in decibels heard by the observer is 97.50 dB.

(a) To find the total amount of energy transferred away from the explosion by sound, we can use the formula:

Energy = Intensity x Time

Substituting the given values:

Energy = (7.20 x 10-2 W/m2) x (0.205 s) = 1.476 x 10-2 Joules

(b) The sound level in decibels heard by the observer can be calculated using the formula:

Sound Level (dB) = 10 x log10(Intensity / Threshold Intensity)

Substituting the given values:

Sound Level (dB) = 10 x log10((7.20 x 10-2 W/m2) / (10-12 W/m2)) = 97.50 dB

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Answer:

The problem can be solved using the equation below

Explanation:

ΔE = E1 − E2

ΔE = 2.179*〖10〗^(-18)*(⁡〖1/〖n_1〗^2 〗-⁡〖1/〖n_2〗^2 〗 )

Answer: 996m/s

Explanation:

Formula for calculating velocity of wave in a stretched string is

V = √T/M where;

V is the velocity of wave

T is tension

M is the mass per unit length of the wire(m/L)

Since the second wire is twice as far apart as the first, it will be L2 = 2L1

Let V1 and V2 be the speed of the shorter and longer wire respectively

V1 = √T/M1... 1

V2 = √T/M2... 2

Since V1 = 249m/s, M1 = m/L1 M2 = m/L2 = m/2L1

The equations will now become

249 = √T/(m/L1) ... 3

V2 = √T/(m/2L1)... 4

From 3,

249² = TL1/m...5

From 4,

V2²= 2TL1/m... 6

Dividing equation 5 by 6 we have;

249²/V2² = TL1/m×m/2TL1

{249/V2}² = 1/2

249/V2 = (1/2)²

249/V2 = 1/4

V2 = 249×4

V2 = 996m/s

Therefore the speed of the wave on the longer wire is 996m/s

Final answer:

The speed of the wave on the longer wire would be the same as on the shorter wire, which is 249 m/s, because the tension and linear mass density are the same.

Explanation:

The speed of a transverse wave on a string is determined by the tension of the string and the linear mass density of the string, according to the formula v = √{Ft/mu}, where v is the wave speed, Ft is the tension in the string, and \\mu is the linear mass density. Since both wires have the same mass and tension, the linear mass density is the same. Therefore, the speed of the wave on the longer wire would be the same as that on the shorter wire, which is 249 m/s.

Answer:

d.interpretation of sensory information

Explanation:

The organizing, recognition, and understanding of sensory information is perception(the Latin perceptio). It is the experience in order to represent and comprehend the knowledge as well as the world.It comprises data collection from sensory organs to brain interpretation

Answer:

1) 2.44 joules

2) 7.73 m/s

3) 7.6 joules

Explanation:

Kinetic energy (K) of a particle is:

[tex] K=\frac{mv^{2}}{2} [/tex] (1)

with m the mass, and v the velocity

1) Because we already now velocity on A (va) and the mass of the object we can calculate its kinetic energy:

[tex]K_{a}=\frac{mv_{a}^{2}}{2}=\frac{(0.338kg)(3.8\frac{m}{s})^{2}}{2}=2.44J [/tex]

2) Because on B we know mass and kinetic energy we should solve (1) for v and use our values to find the velocity on B:

[tex]v_{b}=\sqrt{\frac{2K_{b}}{m}}=\sqrt{\frac{2(10.1J)}{(0.338kg)}}=7.73\frac{m}{s} [/tex]

3) Work-energy theorem states that the change of kinetic energy of an object is equal to the total work done on it, so:

[tex]W=K_b-K_a=10.1J-2.44J= 7.6J [/tex]

Answer: The question is incomplete or missing details. here is the remaining part of the question ;

1. impossible to determine

2. half of Isaac’s

3. the same as Isaac’s

4. twice Isaac’s

The angular speed of feng will be the same as that of Isaac. Hence the answer is option 3

Explanation:

Since we have been told that both feng and isaac are riding on a merry go round i.e in a circular motion, irrespective of how fast one ride above the other, the angular speed will be constant since they are riding on a merry go round, as such both feng and isaac will maintain equal angular speed, hence the angular speed of feng will be the same as that of Isaac.

When the merry-go-round is rotating at a constant angular speed, what is Feng’s angular speed will be same as Isaac's.

Since, both Feng and Isaac are riding on the same marry-go-round in a circular motion. The speed of the marry-go-round is constant.

Angular speed depends on the frequency of the rotation and frequency of the rotation is irrespective of the position in a circle.

Therefore, when the merry-go-round is rotating at a constant angular speed, what is Feng’s angular speed will be same as Isaac's.

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Final answer:

When you see a crescent Moon, only a small portion of the Moon's surface is in daylight due to the angle of sunlight. The rest is faintly illuminated by Earthshine.

Explanation:

Crescent Moon: When you see a crescent Moon, only a small portion of the Moon's entire surface is in daylight. The illuminated portion of the Moon's surface is determined by the angle at which sunlight strikes the Moon. The rest of the Moon's surface not in direct sunlight is faintly illuminated by Earthshine, caused by sunlight reflecting off the Earth.

Answer:

3 units

Solution:

V=539 cubic units

Square base, with edge a=7 units

Slanted edge length: s=14 units

V=Ab h

Ab=49 square units

539 cubic units = (49 square units) h

h= 11 units

s-h=14 units-11 units

s-h=3 units

Answer:

3 units

Explanation :

Volume of an oblique rectangular prism with a square base = A×B×h

Where h = perpendicular height

From the question, Volume of an oblique rectangular prism with a square base = 539 cubic units

We were asked from the question to find how many units longer the slanted edge length of the prism, 14 is compared to its perpendicular height.

The first step is : Find the perpendicular height

Edges A = 7 units

Edges B = 7 units

Perpendicular height ?

Hence,

539 = 7 × 7 × h

539 = 49h

h = 539 ÷ 49

h = 11 units

Therefore, perpendicular height of the prism = 11 units

To find how many units longer, we would subtract the perpendicular height of the prism from the slanted edge length of the prism

= 14 units - 11 units

= 3 units .

Therefore the slanted edge length of the prism , 14, is 3 units longer compared to its perpendicular height.

Final answer:

Alice and Tom will both have the same speed upon reaching the water because gravity accelerates them both at the same rate for their vertical descent. Alice's initial horizontal velocity does not affect her vertical downward acceleration.

Explanation:

The correct answer is C) they will both have the same speed. This is because their vertical descent is solely affected by gravity, which accelerates all objects at the same rate (approximately 9.8 m/s2) regardless of their horizontal velocity component. Alice's initial horizontal velocity of 25 m/s contributes only to her horizontal movement and does not affect the rate at which she falls vertically due to gravity. Consequently, both Alice and Tom will have the same vertical speed when they reach the lake. When you consider both vertical and horizontal components for Alice, her overall splashdown speed will be greater than Tom's; however, the question asks about just the speed. Since only the vertical descent is mentioned, we infer that it's the vertical component being considered. Therefore, their speeds, considering just their vertical motion under gravity, are the same.

Answer:

x = 54.3m (on the +ve x axis)

Explanation:

This is an Initial Value Problem. That means the initial values of certain parameters have been given and that can help solve the problem.

Given that acceleration, a, is:

ax(t) = - 0.032(15.0 - t)

And the initial values are:

x(t = 0) = - 14.0m

v(t = 0) = 8.7m/s

Hence,

a = - 0.032(15 - t)

a = - 0.48 + 0.032t

a = dv/dt = -0.48 + 0.032t

To obtain the velocity, v, integrate the acceleration and apply the initial values of v and t:

v = ∫dv/dt  = ∫(-0.48 + 0.032t)

∫dv = ∫(-0.48 + 0.032t)dt

(v - v₀) = -0.48(t - t₀) + 0.032(t²/2 - t₀²/2)

Inputting the initial values t₀ = 0s, v₀ = 8.7m/s:

=> v - 8.7 = -0.48t + 0.032t²/2

v = 8.7 - 0.48t + 0.016t²

To obtain distance, x, integrate the velocity and apply the initial values:

v = dx/dt = 8.7 - 0.48t + 0.016t²

=> ∫dx/dt = ∫(8.7 - 0.48t + 0.016t²)

∫dx= ∫(8.7 - 0.48t + 0.016t²)dt

(x - x₀) = 8.7(t - t₀) - 0.48(t²/2 - t₀²/2) + 0.016(t³/3 - t₀³/3)

Inputting the initial values t₀ = 0s, x₀ = - 14.0m:

(x + 14.0) = 8.7t - 0.48t²/2 + 0.016t³/3

x = 8.7t - 0.48t²/2 + 0.016t³/3 - 14.0

Now that the distance, x, has been obtained, when t = 10s:

x = 8.7*10 - 0.48*10²/2 + 0.016*10³/3 - 14.0

x = 87 - 24 + 5.3 - 14.0

x = 54.3m

Therefore, at time, t = 10s, x = +54.3m. (i.e. 54.3 on the +ve x axis).

Acceleration of a body is the change in velocity with respect to time.

The x-coordinate of the object when value of time is 10 second is 54.3 m.

Acceleration of a body is the change in velocity with respect to time.

Given information-

A small object moves along the x-axis with acceleration,

[tex]ax(t)=-0.0320(15-t)[/tex]

Initial position and initial velocity of the object is,

[tex]x_0=-14\rm m\\v_0=8.7\rm m/s[/tex]

For the velocity integrate the given equation as,

[tex]ax(t)=-0.0320(15-t)\\\dfrac{dv}{dt} =\int ({-0.48+0.032t} )\, dt\\v-v_0=-0.48t+0.032\times\dfrac{t^2}{2} \\v-8.7=-0.48t+0.016t^2\\v=0.016t^2-0.48t+8.7[/tex]

Integrate it again to find the distance of the object.

[tex]v=0.016t^2-0.48t+8.7\\\int\dfrac{dx}{dt}=\int(0.016t^2-0.48t+8.7)dt\\x-x_0=0.016\times\dfrac{t^3}{3}-0.48\times\dfrac{t^2}{2}+8.7t\\x-14=0.016\times\dfrac{t^3}{3}-0.48\times\dfrac{t^2}{2}+8.7t\\\\x=0.016\times\dfrac{t^3}{3}-0.48\times\dfrac{t^2}{2}+8.7t-14\\[/tex]

Put the value of [tex]t[/tex] as 10 seconds as,

[tex]x=0.016\times\dfrac{10^3}{3}-0.48\times\dfrac{10^2}{2}+8.7\times10-14\\[/tex]

[tex]x=54.3\rm m[/tex]

Hence the x-coordinate of the object when value of time is 10 second is 54.3 m.

Learn more about the acceleration here;

https://brainly.com/question/11021097

Answer:

Explanation:

Given

average velocity of stream is [tex]v_{avg}=3\ m/s[/tex]

Stage of stream i.e. depth [tex]d=14\ m[/tex]

width of stream [tex]w=27\ m[/tex]

We know that discharge of a stream is given by

[tex]Q=A\cdot v[/tex]

where A=area of cross-section

v=average velocity

[tex]A=14\times 27\ m^2[/tex]

Therefore discharge is given by

[tex]Q=14\times 27\times 3[/tex]

[tex]Q=1134\ m^3/s[/tex]