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The celing of a long hall is 25 m high, ...

The celing of a long hall is 25 m high, What is the maximum horizontal distance that a ball thrown with a speed of `40ms^(-1)` can go without hitting the ceiling of the hall?

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Suppose the ball is thrown with speed u at an antle `theta _(0)` with the horizontal. Then the maximum eight attained by the ball is : `sin ^(2) theta _(0) = ( 2 gh)/( u ^(2)) = (2 xx 9.8 xx 25)/((40 ) ^(2))`
`sintheta _(0) = (0.5534)`
`theta _(0)= sin^(-1) (0.5534)= 33.6 ^(@)`
The maximum horiontal distance which the ball can go is given by :
`R = ( u ^(2) sin 2 theta _(0))/( g ) = ( (u _(0)) ^(2) . sin ^(2) ( 2xx 33.6))/(9.8)`
`= (( u _(0) ) ^(2) sin 67.2 ^(@))/( 9.8) = (1600 xx 0.9219)/(9.8)`
`= 150.5 m`
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