# calculus

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A person drops a stone from a bridge. How high is the bridge if they hear the splash 4 seconds later. Assume the speed of sound is 1080ft/sec.

• calculus -

d = 1/2 at^2 = 16t^2
t = sqrt(d)/4

total time = falling time + echo time
4 = sqrt(d)/4 + d/1080

Let s = sqrt(d)

s^2 + 270s - 4320 = 0
s = 15.15
d = 229.52 ft

Check:
falling time = sqrt(229.52/16) = 3.7875
echo time = 229.52/1080 = 0.2125
total: 4 seconds

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