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

Neglecting air resistance, the equation is

d = 1/2 a t^2

a, acceleration from gravity, is 9.8 m/sec^2
t, time, is 5 sec
d = 1/2 9.8 * 5 * 5

d = 122.5 meters
----------------------
v = at

v = 9.8 * 5
v = 49 m/sec

Answer 2

Keith P, you forgot that the package was flying together with the plane, so it does not fall vertically, instead, we have horizontal hit. The horizontal component vx of the package's velocity is that of the airplane (neglecting air resistance) and the vertical component is the one you calculated (vy = 49 m/s). The magnitude of the velocity is therefore v^2 = vx^2 + vy^2 or the speed of the package when it hits the ground v = 206 m/s.

Answer 3

It was dropped from an altitude of 336 ft AGL and was traveling vertically at a velocity of 128 ft/sec, but I have no idea on the horizontal component. (The above assumes no significant drag generated by the package.) Remember, the time from release to impact is independent of the horizontal velocity at release.

Answer 4

Not that high, and pretty fast

Answer 5

35,000 feet