An airplane is flying at a speed of 200 m/s in level flight at an altitude of 800m. A package is to be dropped from the plane to land on a target on the ground.
At what horizontal distance away from the target should the package be released so that it lands on the target?
When the package is dropped it has the horizontal velocity of the airplane. So it will travel some distance at horizontal also while it is coming down. So the airplane should drop the package before the target instead of releasing it directly on top of it.By the time it reaches ground it has travelled 800m vertically under gravity if air resistance is neglected.
using equations of motion;
`darrs = ut+1/2at^2`
At the moment of drop the package only has horizontal velocity component because the the speed of airplane.
`800 = 0+1/2xx9.81xxt^2`
`t = 12.77s`
So in this 12.77 seconds the package travels horizontally with a velocity of 200m/s.
`rarrs = ut+1/2at^2`
There is no acceleration in the` rarr` direction.
`s = 200xx12.77`
`s = 2554m`
So the airplane must drop the package 2554m before the target.