Question

An airplane pilot is moving with a velocity v and drops a package. In the absence of air resistance, where is the package relative to the airplane at the moment it hits the ground?

Option 1: Behind the airplane
Option 2: In front of the airplane
Option 3: Directly below the airplane
Option 4: Cannot be determined without knowing how high the plane

Answer 1

In the absence of air resistance, a package dropped by an airplane will land directly below the point where it was released, because it maintains the same horizontal velocity as the airplane until impact.

Step-by-step explanation:

If an airplane pilot drops a package while moving with a velocity of v and in the absence of air resistance, the package when it hits the ground will be directly below the airplane. This is because when the package is released, it will continue to have the horizontal velocity of the airplane due to its inertia. There is no horizontal force acting on the package (since we're ignoring air resistance), so it does not fall behind. It only accelerates downward due to gravity. When the package impacts the ground, its position relative to the airplane depends only on the horizontal motion since both the plane and the package are moving forward at the same velocity. Therefore, the package will hit the ground directly below the point where it was dropped, assuming no significant horizontal forces act on it after release.