A boy standing on the top of a tower 36 m high has a throw a packet to his friend standing on the ground 48 m horizontally away. If the throws a packet directly aiming the friend with a speed of `10 ms^(-1)`, how short will be packet fall ?

Explanation

The packet will strike at point C instead of reaching to friend B because the packet will move on a parabolic path instead of straight line.

From geometry, `tan theta = (36)/(48) = (3)/(4)`
`rArr sin theta = (3)/(5), cos theta = (4)/(5)`

For to C, `S_(y) = u sin theta t +(1)/(2) g t^(2) rArr 36 = 10 xx (3)/(5) t +(1)/(2) xx 10 t^(2) = 6t +5t^(2) rArr 5t^(2) +6t - 36 = 0`
At `t = 2.15s, S_(x) = u cos theta t = 10 xx (4)/(5) xx 2.15 = 17.2 m = AC :. BC = AB - AC = 48 - 17.2 = 30.8 m` ltbr. The packet will fall at distance `30.8`m infront of his friend.