How high above the ground is the plane flying?

Question

An airplane is flying horizontally at 200 m/s, and it drops a care package to some people on the ground below. If the package takes 5 seconds to hit the ground, how high above the ground is the plane flying? Also what is the speed of the package when it hits the ground?

Answer 1

The general formula for change in position is xf = 1/2 at^2 + v0 t + x0.

Consider the vertical motion first.

a = negative g (negative is usually defined as down)
v0 = 0 (no vertical motion at drop point)
x0 = height (your goal)
xf = 0 (the ground)

Solve the quadratic equation (this is a simple one) to get the height.

For velocity vf = v0 + at

Do this for the vertical motion to get your vertical velocity at impact.

Do it for horizontal motion (easy because there's no horizontal acceleration if you have no air resistance) to get the horizontal velocity at impact (same as initial).

Use pythagorean theorem to combine components of velocity to get final speed.