There are two parts to this solution: The down part for the helmet, and the up part for the sound. The down part has to be solved first, before the up part.
-- The helmet falls 78.4 meters. How long does that take ?
In gravity,
Distance = (1/2) (acceleration) (Time²)
78.4 m = (1/2) (9.8 m/s²) (Time²)
Time² = (78.4 m) / (4.9 m/s²)
Time² = 16 sec²
Time = 4 seconds.
-- The crew heard the sound of helmet hitting the ground 4.23 seconds after their buddy dropped it.
We just calculated that it took 4 seconds for it to hit the ground.
So it took 0.23 second for the sound of the clunk to propagate the 78.4 meters back up to them. What's that speed ?
Speed = (distance) / (time)
Speed = (78.4 m) / (0.23 sec)
<em>Speed = 340.9 m/s</em>
<u>Acceleration = (change in speed) / (time for the change)</u>
(Note: That's all the Physics there is to this problem.
The rest is all arithmetic.)
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change in speed = (40 - 20) miles/hour = -20 miles/hour
time for the change = 10 minutes
Acceleration = (-20 miles/hour) / (10 minutes) =
<em>-2 miles/hour per minute</em> .
That's a perfectly good and technically correct expression for acceleration.
But obviously the units might make some people dizzy. So let's try to
clean it up a little.
Notice that 10 minutes is 1/6 of an hour.
So we could write the acceleration as
Acceleration = (-20 miles/hour) / (1/6 hour) = -120 miles/hour per hour =
<em>-120 miles/hour² .</em>
You could convert this into any units you like. It's really not a physics problem
any more, it's just an exercise in converting units.
B was fired first and just trust me