I am stuck on this problem and would be really greatful with any help on it. Thanks a bunch!
A stone is dropped from rest into a welll. The sound of the splash is heard exactly 1.90 s later. Find the depth of the well (in m) if the air temperature is 14.0°C.
2006-12-05 15:34:48 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Physics
I have no idea why the air temperature is given, but the depth of the well is as follows:
a = -9.8 m/sec²
v = -9.8t (initial velocity = 0)
y = -4.9t² (initial position = 0)
Solve for y:
y = -4.9*1.9² = -17.689 m
The well is 17.689 m deep.
2006-12-05 15:38:48 · answer #1 · answered by computerguy103 6 · 0⤊ 1⤋
The problem wants you to take into account the speed of sound in air as well as the usual s = 0.5gt^2 business. The time delay of the sound is small, so figure the depth of the well ignoring it. The speed of sound is 339.8 m/sec [from table, by interpolation], so divide the distance by that number and subtract from 1.9 seconds to allow for it, and re-calculate s as above. There is a tiny residual error in this procedure which can be ignored.
2006-12-05 23:48:45 · answer #2 · answered by Anonymous · 0⤊ 0⤋
The answer is s = at²/2 where a is acceleration of gravity (9.8 m/s²), t is time (in seconds), and a is distance (in meters). Using this, we get s = 17.689 m.
I'm not real sure why the air temperature is included in the problem since the speed of sound is also effected by atmospheric pressure and humidity.
Doug
2006-12-05 23:49:36 · answer #3 · answered by doug_donaghue 7 · 0⤊ 0⤋
at 14 C the speed of sound is 339.94 m/s
--> http://hyperphysics.phy-astr.gsu.edu/hba...
in 1.9 seconds sound will travel 645.886 meters
The well is a little less deep than that because it also takes some time for the stone to drop to the water below.
s = 1/2 at^2
Source(s):
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2006-12-05 23:37:26 · answer #4 · answered by DanE 7 · 0⤊ 0⤋