The ceiling of a long hall is 25 m high . What is the maximum horizontal distance that a ball thrown with a speed of 40 m / s can go without hitting the ceiling of the hall ? ( g = 10 m / s2 )

Asked by monikalakhara.1995 | 26th Jun, 2021, 08:30: PM

Expert Answer:

Maximum height h reached by ball is determined from the following equation
 
begin mathsize 14px style h space equals space fraction numerator u squared sin squared alpha over denominator 2 space g end fraction end style  ......................(1)
where  u = 40 m/s is initial projection speed , α is angle of projection and g is acceleration due to gravity
 
From eqn.(1) , we get angle of projection α as follows
 
begin mathsize 14px style sin alpha space equals space square root of fraction numerator 2 space g space h over denominator u squared end fraction end root space equals space square root of fraction numerator 2 space cross times space 10 space cross times space 25 over denominator 40 cross times 40 end fraction end root space equals space 0.559 end style
Hence angle of projection α = sin-1 (0.559 ) = 34o 
 
Maximum Range R is determined from following equation 
 
begin mathsize 14px style R space equals space fraction numerator u squared sin left parenthesis 2 alpha right parenthesis over denominator 2 g end fraction space equals space fraction numerator 40 cross times 40 cross times sin left parenthesis 68 right parenthesis over denominator 2 cross times 10 end fraction space equals space 74.17 space m end style

Answered by Thiyagarajan K | 26th Jun, 2021, 09:17: PM