A stone is dropped from the top of a tower 500 m high into a pond of water at the base of the tower. When is the splash heard at the top? Given, g = 10 m s−2 and speed of sound = 340 m s−1.
Question
A stone is dropped from the top of a tower 500 m high into a pond of water at the base of the tower. When is the splash heard at the top? Given, g = 10 m s−2 and speed of sound = 340 m s−1.
Solution
To determine when the splash is heard at the top of the tower, we need to consider the time it takes for the stone to fall and the time it takes for the sound of the splash to travel back up to the top.
First, let's calculate the time it takes for the stone to fall from the top of the tower to the pond. We can use the equation of motion:
s = ut + (1/2)gt^2
where s is the distance, u is the initial velocity (which is 0 since the stone is dropped), g is the acceleration due to gravity, and t is the time.
In this case, the distance is 500 m and the acceleration due to gravity is 10 m/s^2. Plugging in these values, we can solve for t:
500 = 0*t + (1/2)10t^2 500 = 5t^2 t^2 = 100 t = 10 s
So it takes 10 seconds for the stone to fall from the top of the tower to the pond.
Next, let's calculate the time it takes for the sound of the splash to travel back up to the top of the tower. We can use the equation:
v = d/t
where v is the speed of sound and d is the distance traveled by the sound. In this case, the speed of sound is 340 m/s and the distance traveled is 500 m (the height of the tower). Plugging in these values, we can solve for t:
340 = 500/t t = 500/340 t ≈ 1.47 s
So it takes approximately 1.47 seconds for the sound of the splash to travel back up to the top of the tower.
Finally, to find the total time it takes for the splash to be heard at the top, we add the time it takes for the stone to fall to the time it takes for the sound to travel:
Total time = 10 s + 1.47 s Total time ≈ 11.47 s
Therefore, the splash is heard at the top of the tower approximately 11.47 seconds after the stone is dropped.
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