The ceiling of a long hall is 25m high. What is the maximum horizontal distance that a ball thrown with speed of 40 m/s can go without hitting the ceiling of the hall? from Physics Motion in A Plane Class 11 Manipur Board
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The ceiling of a long hall is 25m high. What is the maximum horizontal distance that a ball thrown with speed of 40 m/s can go without hitting the ceiling of the hall?

Height of the ceiling = 25 m = MAximum height attained by the ball. 

Velocity of the ball, u = 40 m/s

Maximum height is given by, straight H equals fraction numerator straight u squared sin squared straight theta over denominator 2 straight g end fraction

i.e., sin squared straight theta space equals space fraction numerator 2 gH over denominator straight u squared end fraction equals fraction numerator 2 cross times 9.8 cross times 25 over denominator left parenthesis 40 right parenthesis squared end fraction equals 0.30625

∴       sin space straight theta space equals space square root of 0.30625 end root space equals space 0.5534 

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#13 {main}</pre>          straight theta equals 33.6 

∴ Maximum horizontal distance,

     straight R equals fraction numerator straight u squared sin space 2 straight theta over denominator straight g end fraction equals fraction numerator left parenthesis 40 right parenthesis squared space sin space 67.2 over denominator 9.8 end fraction 
       equals space 150.5 space straight m.                                    
               
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