This problem incorporates the main idea of gravitational freefall, but also adds an extra to it, and I get different answers from the back of the book:(adsbygoogle = window.adsbygoogle || []).push({});

A rock is dropped from a sea cliff, and the sound of it striking the ocean is heard 3.2s later. If the speed of sound is 340m/s, how high is the cliff?

Book answer: 46m.

My answer: 52m.

My solution: Because of the lack of information, I simply used variables to substitute.

Given: x0 = 0, a = -9.8m/s^2, total time = 3.2s

x = x0 + v0t + .5at^2 = -4.9t^2 => I changed this to 4.9t^2 to reflect a change in point of reference.

Since the speed of sound is given, and x is assigned as above, I determined that the time in which sound travelled up the cliff is 340/x sec. Since the problem is asking for distance, I swapped the variables around with the length to get the following: t^2 = x/4.9 => (x/4.9)^.5 => time it takes to fall down the cliff.

Given that 3.2 s is the total time for the rock to fall AND for the sound to rebound, I wrote down the following: 3.2 = (340/x) + (x/4.9)^.5 . One calculation led to another, and I got the answer at top. Am I right this far and I got my variable switching wrong, or did I do something fundamentally wrong? Eagle eyes most apprecated :D

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# Homework Help: Free-fall question with extras

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