Question 1068891: Peter drops a stick of dynamite down a deep hole near Spruce Mountain. He times it from the moment he lets go and hears the sound exactly 11.20 seconds later. If the speed of sound is 343 meters / second, how deep is this hole? You must take the speed of sound into consideration. Answer in meters. Use g = 9.8 m/sec^2.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Peter drops a stick of dynamite down a deep hole near Spruce Mountain.
He times it from the moment he lets go and hears the sound exactly 11.20 seconds later.
If the speed of sound is 343 meters / second, how deep is this hole?
You must take the speed of sound into consideration.
Answer in meters. Use g = 9.8 m/sec^2.
:
The stick and the sound travel the same distance; dist = speed * time
let t = stick drop time
then
(11.2-t) = sound travel time
:
4.9t^2 = 343(11.2-t)
4.9t^2 = 3841.6 - 343t
a quadratic equation
4.9t^2 + 343t - 3841.6
Using the quadratic formula, I got a positive solution of
9.82 seconds for the stick to drop
then
11.2 - 9.82 = 1.38 seconds for sound to travel back to the surface
:
Find the depth of the hole
343 * 1.38 = 473 meters deep
:
Check this by using the falling time of the stick
4.9(9.82^2) = 473 meter also
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A student pointed out that my first solution is not correct.
On thinking it over, I should have used 4.9t^2 for a dropped object, not 9.8 as given.
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