Question

a construction workers helmet slips nd falls whn he is78.4 m above the ground. he hears the sound of helmet hitting the ground 4.23 sec aftr it slipped. find the speed of sound in air?

Answer 1

Given

h = 78.4 m

g = 9.8 m/s²

u = 0

Time taken to hear the sound, T = 4.23 sec

v² = u ² + 2gh

= 0 + 2gh

v² =√2gh

v= √2 x 9.8 x 78.4

v= 39.2

this is the speed of the helmet.

Now using,

v = u + gt

39.2 = 0 + 9.8 x t

39.2/9.8 = t

t= 4 sec

therefore time taken by helmet to reach the ground is 4 sec.

T – t = 4.23 – 4 =0.23 s

In this time sound travels the height 78.4 m (distance)

So, speed of sound in air = distance/time

=78.4/0.23

=340.86m/s