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Ivahew [28]
3 years ago
8

A soccer player kicks a rock horizontally off a 37 m high cliff into a pool of water. If the player hears the sound of the splas

h 2.92 s later, what was the initial speed given to the rock (in m/s)? Assume the speed of sound in air is 343 m/s. m/s (b) What If? If the temperature near the cliff suddenly falls to 0°C, reducing the speed of sound to 331 m/s, what would the initial speed of the rock have to be (in m/s) for the soccer player to hear the sound of the splash 2.92 s after kicking the rock?
Physics
1 answer:
Alchen [17]3 years ago
8 0
<h2>Answer:</h2>

<em><u>(a). 16.741 m/s</u></em>

<em><u>(b). 15.75 m/s</u></em>

<h2>Explanation:</h2>

In the question,

Height of the cliff, h = 37 m

Time taken to reach the sound to us = 2.92 s

Speed of the sound in air at room temperature = 343 m/s

Now,

Let us say the speed of the ball = u m/s

So,

Time taken by the ball to reach at the bottom, t is given by,

t=\sqrt{\frac{2h}{g}}\\t=\sqrt{\frac{2\times 37}{9.8}}\\t=2.747\,s

So,

Splash is heard after = 2.92 s

So,

<u>Time taken by sound to travel the shortest distance along the hypotenuse of the triangle</u> thus formed is,

t = 2.92 - 2.747

t = 0.172 s

Now,

Distance traveled by sound is given by,

Distance=343\times 0.172\\Distance=59.02\,m

So,

In the triangle using the Pythagoras Theorem,

Horizontal distance traveled is,

D=\sqrt{59.02^{2}-37^{2}}\\D=45.99\,m

So,

Speed of throwing of ball is given by,

Distance=Speed\times Time\\45.99=u\times 2.747\\u=16.741\,m/s

<em><u>Therefore, the speed of the ball = 16.741 m/s.</u></em>

(b).

If,

Speed of sound = 331 m/s

So,

<u>Distance traveled by sound</u> is,

Distance=331\times 0.172\\Distance=56.932\,m

So,

Distance traveled in the horizontal by ball is,

Distance=\sqrt{56.932^{2}-37^{2}}\\Distance=43.269\,m

So,

Speed of the ball thrown is given by,

Speed=\frac{Distance}{Time}\\Speed=\frac{43.269}{2.747}\\Speed=15.75\,m/s

<em><u>Therefore, the speed of the ball = 15.75 m/s.</u></em>

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The following three hot samples have the same temperature. The same amount of heat is removed from each sample. Which one experi
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Complete Question:

The following three hot samples have the same temperature. The same amount of heat is removed from each sample. Which one experiences the smallest drop in temperature, and which one experiences the largest drop? Sample A: 4.0 kg of water [c = 4186 J/(kg·C°)] Sample B: 2.0 kg of oil [c = 2700 J/(kg·C°)] Sample C: 9.0 kg of dirt [c = 1050 J/(kg·C°)]

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A. Smallest B. Largest.

Explanation:

Assuming no heat exchange except for the heat removed from any sample (which we know is the same for the three ones), and that the process is done using only conduction, we can use the equation that relates the heat lost or gained by one object, with the mass of the object and the consequent change in temperature, as follows:

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As the three expressions must be equal each other, it's clear that the unknown term (the drop in temperature) must compensate the product of the mass times the specific heat.

This product is the following for the three samples:

Water: 4.0 kg*4,186 J/kgºC = 16,744 J/ºC

Oil : 2.0 kg*2,700 J/kgºC    = 5,400 J/ºC

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Clearly, we see that in order to keep the heat exchange equations equal each other, the water must suffer the smallest drop in temperature, and the oil must experience the largest one.

So, the sample A experiencies the smallest drop in temperature, and sample B does the largest one.

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