Physics problem-help needed, not sure what equations to use.

Question

Small-plane pilots regularly compete in "message drop" competitions, dropping heavy weights (for which air resistance can be ignored) from their low-flying planes and scoring points for having the weights land close to a target. A plane 75 m above the ground is flying directly toward a target at 51 m/s.

1. At what distance from the target should the pilot drop the weight?

Answer 1

First calculate the time it takes for the weight to drop. You do that by just thinking about the y-direction. It would be the same as if the weight was dropped while standing still (like off a building).

You would use x = (1/2)at² where a is -9.8 m/s² and x = -75 m (75 meters down to the ground):

x = (1/2)at²

-75 = (1/2)(-9.8)(t²)

-75 = -4.9(t²)

t² = 15.306

t = 3.91 seconds

Then, figure out how far the object will travel in the x-direction during that 3.91 seconds

x = vt where v = 51 m/s

x = (51)(3.91) = 200 meters