physics
posted by wen on .
an object falls from a plane flying horizontally at an altitude of 40,000 ft at 500 mi/h. How long will it take to hit the ground?

At 40,000 ft. air resistance becomes important, as the object will likely reach terminal velocity and greatly increases the time it takes to reach the ground. Also, the horizontal velocity comes into play as the terminal velocity caused by air resistance is actually a terminal speed, so it's the resultant that counts.
The shape of the object is not specified, so any calculation of the terminal velocity remains an estimate with assumptions.
If you have not done airresistance and terminal velocities, read on.
Neglecting air resistance, the horizontal velocity of the plane does not count, and you can calculate the time required as if it were a free fall over short distances.
Let
vi=initial velocity (0)
t=time in seconds,
g=acceleration due to gravity, 32.2 f/s^2
S=vertical distance travelled = 40,000 ft
S=vi*t+(1/2)gt^2
40000=0*t + (1/2)*32.2*t^2
Solve for t to get:
t^2=2*40000/32.2=2484.47
t=50 sec. approx.
(remember: this is by ignoring airresitance) 
87.9s