A boy wants to measure the depth of a well. When he drops a stone from the top o

Question

A boy wants to measure the depth of a well. When he drops a stone from the top of the well, he hears the sound made by the stone hitting the water 1.5 s later. If we can assume that the speed of sound is fast enough to be ignored, how deep is the well? 5.5 m 10 m 11 m 21 m When a ball is launched horizontally with a velocity 5.0 M/s from the deep of a cliff 10 m high, how does it take ball to reach the ground? 1.0 s 1.4 s 2.8 s 3.0 s In the situation described in problem 4, how far horizontally does the ball go away from the cliff when it lands on the ground?

Explanation / Answer

According to the given problem:

C.) Let h be the depth of the well.

g is the acceleration of gravity (9.81 m/s).

v is the speed of sound (340 m/s).

After the rock is released, the time it takes to reach the water is:

t = sqrt (2h / g)

Then, the sound of the splash take a time h/v to travel back.
The total time t = 1.5s is the sum of those two terms:

t = sqrt (2h / g) + h/v

This is a quadratic equation for the unknown x = sqrt(h) > 0
(1/v) x^2 + sqrt(2/g) x - t = 0
We discard the negative solution of that equation and retain the positive one:
x = 3.253
h = x^2 = 10.58 m

D)By using formula s = u*t + 0.5*a*t^2, with u=0, s = 10 m, a = 9.81 m/s^2,

t = sqrt(2 * 10/9.81) = 1.4 s

As the horizontal velocity is constant (considering there is no air friction), the distance it travels = horizontal velocity * time taken to fall 33 m

distance = 5 * 1.4 = 7 m

I think you understand my explanation, and hope you got your solution and glad I can help .Rate me! if you like the solution.

Thank you .

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