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,
[tex]y=\frac{1}{2} gt^2[/tex]
Write an expression for t, the time taken for the package to fall through y.
[tex]t^2=\frac{2y}{g}[/tex]
Substitute 100 m for y and 9.81m/s² for g.
[tex]t^2=\frac{2y}{g}\\ =\frac{2(100m)}{9.81m/s^2} \\ =20.39s^2\\ t=4.52s[/tex]
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,
[tex]x=vt\\ =(150m/s)(4.52s)\\ =678m[/tex]
If the package is released 678m before the target, the package would reach the scientists working in Greenland.
