<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,
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,
So,
In the triangle using the Pythagoras Theorem,
Horizontal distance traveled is,
So,
Speed of throwing of ball is given by,
<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,
So,
Distance traveled in the horizontal by ball is,
So,
Speed of the ball thrown is given by,
<em><u>Therefore, the speed of the ball = 15.75 m/s.</u></em>