A person standing on the top of a tower `36m` high has to 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 m//s`, how short will the packet fall ?

Explanation

The packet will strike at point `B` instead of reaching ti friend `P`, because the packet will move on a parabolic path instead of straight line.


From geometric, `tan theta = (36)/(48) = (3)/(4) rArr sin theta = (3)/(5), cos theta = (4)/(5)`
`O` to `B`:
`y: y = u sin theta t + (1)/(2) g t^(2)`
`36 = 10 xx (3)/(5)t + (1)/(2) xx 10 t^(2) = 6t + 5t^(2)`
`5t^(2) + 6t - 36 = 0 rArr t = 2.15 s`
`x: x = u cos theta t = 10 xx (4)/(5) xx 2.15 = 17.2 m = AB`
`BP = AP - AB = 48 - 17.2 = 30.8 m`
The packet will fall at distance `30.8 m` in front of his friend.