How long before the box hits the ground?

[unidentified4789]

A plane is traveling at 100m/s when it drops a box at an elevation of 2000 meters. How much time is required for the box to reach the earth?

 

[russ_watters]

You know the equation for freefall? Apply it to find the time and multiply the time by the speed of the plane.

 

[HallsofIvy]

What assumptions are you making? Are you ignoring air resistance? (If not, then you will have to state what the air resistance is.)

Assuming no air resistance, 2000 m is low enough that we can ignore the change in gravitational force due to change in distance so: the acceleration is 9.8 m/s². The downward speed after time t is 9.8 t m/s and the distance fallen is 4.9 t². The box will hit the Earth when 4.9 t²= 2000.

The information about the horizontal speed of the airplane (and therefore the horizontal speed of the box) is irrelevant. The time to hit depends only on vertical acceleration and speed.

 

[russ_watters]

As someone informed me in a pm, I misread the problem. Sorry. Halls had it right. I was thinking of how far the box would move forward.