A construction 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 on air

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Solution

Dear Student

$G i v e n, h = 78.4 m g = 9.8 m / s 2 u = 0 T i m e t a k e n t o h e a r t h e s o u n d, T = 4.23 s e c v^{2} = u^{2} + 2 g h = 0 + 2 g h v = \sqrt 2 g h v = \sqrt 2 x 9.8 x 78.4 v = 39.2 T h i s i s t h e s p e e d o f t h e h e l m e t . N o w u \sin g, v = u + g t 39.2 = 0 + 9.8 x t 39.2 / 9.8 = t t = 4 s e c T h e r e f o r e t i m e t a k e n b y h e l m e t t o r e a c h t h e g r o u n d i s 4 s e c . T - t = 4.23 - 4 = 0.23 s I n t h i s t i m e s o u n d t r a v e l s t h e h e i g h t 78.4 m (d i s \tan c e) S o, s p e e d o f s o u n d i n a i r = d i s \tan c e / t i m e = 78.4 / 0.23 = 340.86 m / s$

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

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