A worker's helmet slips and falls when he is 78.4 m above the ground. He hears the sound of the helmet hitting the ground 4.23 seconds after it slipped. Find the speed of sound in air.

Explanation

Acceleration of the helmet, `g=9.8 m s^(-2)`
Distance covered by the helmet, d= 78.4 m
Time of motion of helmet, `t_(1)` = ?
Velocity of sound, v= ?
Time taken by sound travel a distance d, `t_2 = 4.23 - t_(1)`
We have, for motion of helmet
`d= 1/2 gt_(1)^2`
`t_(1)= 4 s`
For propagation of sound
`d= vt_2`
`78.4 = v(4.23 - t_(1))`
`v = 340.8 m s^(-1)`