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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.
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Solution
Height of the stone h = 500 m, g = 10 ms−2
Initial speed of the stone u = 0
Time taken by the stone to reach the surface of water from the top of the tower = t1
∴ h (= S) = ut1 + `1/2"gt"_1^2`
500 m = `0 xx "t"_1 + 1/2 xx 10 xx "t"_1^2`
⇒ 500 = `5 xx "t"_1^2`
⇒ `"t"_1^2 = 500/5`
⇒ `"t"_1^2` = 100
⇒ t1 = `sqrt100`
= 10 s
Total time taken by sound to reach the top of the tower after splash heard = t2
∴ t2 = `"Distance"/"Speed"`
= `h/V`
= `500/340`
= 1.47 s
Total time taken by sound to reach the top of the tower after splash heard
t = t1 + t2
= 10 + 1.47
= 11.47 s1
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