Question

A supply plane needs to drop a package of food to scientists working on a glacier in greenland. the plane flies 100 m above the glacier at a speed of 150 m/s. how far short of the target should it drop the package

Answer 1

The package should be dropped 678 m short of the target.

A package dropped from a plane which is moving at a speed v, has a horizontal velocity equal to the horizontal velocity of the plane. It has a parabolic trajectory, traversing a horizontal range x while it falls through a vertical height y.

The package has no initial vertical velocity, and it falls through a height y under the action of the acceleration due to gravity g.

Use the equation,

$y=\frac{1}{2} gt^2$

Write an expression for t, the time taken for the package to fall through y.

$t^2=\frac{2y}{g}$

Substitute 100 m for y and 9.81m/s² for g.

$t^2=\frac{2y}{g}\\ =\frac{2(100m)}{9.81m/s^2} \\ =20.39s^2\\ t=4.52s$

In the time t  the package travels a horizontal distance x. The horizontal velocity of the package remains constant, since no force acts along the horizontal direction.

Therefore, the horizontal distance traveled by the package is given by,

$x=vt\\ =(150m/s)(4.52s)\\ =678m$

If the package is released 678m before the target, the package would reach the scientists working in Greenland.