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Tire ceiling of a long hall is 25 m high...

Tire 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^-1` can go without hitting the ceiling of the hall ?

Text Solution

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We are given : `H = 25 m , u = 40 ms ^(-1)`
We know that maximum height , `H = ( u ^(2) sin ^(2) theta)/( 2 g)`
`implies 25 = ( ( 40) ^(2) xx sin ^(2) theta)/( 2 xx 9.8 ) implies sin ^(2) theta = ( 490)/( 1600)`
`implies sin theta = 0.5534implies theta = 33. 6 ^(@)`
Also `R = ( u ^(2) sin 2 theta)/( g ) = (( 40) ^(2) sin 2 ( 33. 6))/( 9 .8 ) = (( 40 ) ^(2) sin 67 . 2)/( 9. 8) implies R = 150. 5 m.`
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