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)
Speed = 340.9 m/s
