Asoccer player kicks a rock horizontally off a 37 m high cliff into a pool of water. if the player hears the sound of the splash 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?

(a). 16.741 m/s

(b). 15.75 m/s

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,

So,

Splash is heard after = 2.92 s

So,

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

t = 2.92 - 2.747

t = 0.172 s

Now,

Distance traveled by sound is given by,

So,

In the triangle using the Pythagoras Theorem,

Horizontal distance traveled is,

So,

Speed of throwing of ball is given by,

Therefore, the speed of the ball = 16.741 m/s.

(b).

If,

Speed of sound = 331 m/s

So,

Distance traveled by sound is,

So,

Distance traveled in the horizontal by ball is,

So,

Speed of the ball thrown is given by,

Therefore, the speed of the ball = 15.75 m/s.