The package should be dropped <u>678 m</u> 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,
Write an expression for t, the time taken for the package to fall through y.
Substitute 100 m for y and 9.81m/s² for g.
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,
If the package is released <u>678m</u> before the target, the package would reach the scientists working in Greenland.