Question

a stone is dropped from top of tower 500m high into pond of water at bottom. when is splash heard at the top?

Answer 1

The height of the tower (h) = 500 m

Let t be the time taken by the stone to reach the water surface.

As you know, for a free fall, h = ut + 0.5gt2

Here, initial velocity is zero as the ball is just dropped. 

So, 500 = 0.5× 10× t2 

Therefore, t = 10 seconds.

The speed of sound = 340 m/s

So, the time taken for the sound to travel 500m upwards = 500/340 = 1.47 seconds.

The total time taken to hear the splash sound after dropping the stone = 10 + 1.47 = 11.47 seconds.

Answer 2

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Height of the tower, s = 500 m

Velocity of sound, v = 340 m sˆ’1

Acceleration due to gravity, g = 10 m sˆ’2

Initial velocity of the stone, u = 0 (since the stone is initially at rest)

Time taken by the stone to fall to the base of the tower, t1

According to the second equation of motion:

$\rm S = ut_1 + 1/2 g t_1^2$

$\rm 500 = 0 \times t_1 + 1/2 \times 10 \times t_1^2$

$\rm t_1^2 = 100$

$\rm t_1 = 10s$

Now, time taken by the sound to reach the top from the base of the tower,

$\rm t_2= 500/340 = 1.47 s$

Therefore, the splash is heard at the top after time, t

Where, $\rm t= t_1 + t_2 = 10 + 1.47 = 11.47 s.$