A construction worker's helmet slips and falls when he is 78.4m above the ground.He hears the sound of helmet hitting the ground 4.23 s after it slipped Find the speed of sound in air.
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HELLO DEAR,H =78.4 meter
g=9.81m/s²
u=initial spped=0
TIME TAKEN TO HEAR THE SOUND = τ = 4.23 sec
a) Speed of helmet (v = ?)
Use kinematics engine (free fall)
v 2 = u 2 + 2gh
= 0 + 2gh
Time taken by helmet to reach the ground is t = ?
Use kinematics egh.
v = u + gt
τ-t =4.23-3.99 =0.24s
In this time sound travels the height 78.4 m
So, speed of sound in air =
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Let t be the time taken by the helmet to reach the ground.
We have,
Here,
u = 0, h = 78.4 m, g = 9.8 m/s²
∴ the time taken by the helmet to reach the ground = 4 secs.
The time taken by sound to travel 78.4 m = ( 4.23 - 4 ) s
⇒ 0.23 secs.
∴ the speed of sound in air = 78. 4 / 0.23 m/s
= 341 m/s.