Posted by Gary on Wednesday, June 30, 2010 at 8:55pm.
Write an equation for the time it takes for the rock to hit water, PLUS the time for the sound of the splash to come bace. You know the total time; solve for the height, H. Use a suitable speed of sound, such as 340 m/s; you would need to assume a temperature for a more accurate value of the sound speed.
3.5 (seconds) = H/340 + sqrt (2H/g)
[3.5 - (H/340)]^2 = H/4.9
12.25 - .02059H + 8.65*10^-6 H^2
= 0.2041 H
8.65*10^-6 H^2 -0.2247H - 12.25 = 0
There will be two answers; take the positive root. Also verify my numbers.
Write an equation for the time it takes for the rock to hit water, PLUS the time for the sound of the splash to come bace. You know the total time; solve for the height, H. Use a suitable speed of sound, such as 340 m/s; you would need to assume a temperature for a more accurate value of the sound speed.
3.5 (seconds) = H/340 + sqrt (2H/g)
[3.5 - (H/340)]^2 = H/4.9
12.25 - .02059H + 8.65*10^-6 H^2
= 0.2041 H
8.65*10^-6 H^2 -0.2247H - 12.25 = 0
There will be two answers; take the positive root. Also verify my numbers.
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