Free Fall Facts and Sample Problems

Example:   A crate of food supplies is dropped from an airplane flying  horizontally at 56 m/s (about 125 miles an hour). The altitude of the plane is 2 E 2 meters. There will be total parachute failure due to the old rotten parachutes that have to be used. How many meters short of the target area must the crate be dropped to insure a hit.

 Fact:    As the crate falls, it still maintains a horizontal speed of 56 m/s.

 Fact:    The horizontal motion of a falling object is independent of the downward (vertical) motion of the object.

 Fact:    When the crate strikes the earth, the plane will be directly over the point of impact since the crate and the plane have the same horizontal speed. The plane may not accelerate after dropping the crate.

 Fact:    If the crate were dropped from the plane when the plane was directly above the target, the crate would never hit the target. The crate's horizontal speed would cause the crate to travel 'down range' by the time it touched the ground.

 Step 1: Determine the amount of time it takes the crate to reach the earth.

                t = Ö2d/g    à     Ö(2 * 2 E 2 m)/9.8 m/s² =  Ö 40.8 s²  =  6.4 s

 Step 2:  Determine the horizontal distance achieved by the crate and the airplane in 6.4 seconds.

                  d = V_av * t   à    56 m/s  * 6.4 s  =  358 m

 Summary:      By the time the crate has reached the starving shipwrecked crew, both the airplane and the crate would have traveled a horizontal distance of 358 m. In order to insure a direct hit on the target, the crate should be dropped 358 m up range of the target area. Flying slower and/or at a lower altitude would make this task much easier.

 Sample Problems:

 1. A large rock is dropped from a bridge into the river below.

a) if the time required to fall is 1.7 seconds, with what velocity, in m/sec, does it hit the water?
 b) what is the height, in meters, of the bridge above the water?

 2. How many seconds does it take a metal ball to drop 400 m from rest? What velocity does it achieve?

 3.  A suitcase is accidentally dropped from an airplane flying at an altitude of 1 E 4 m. With what final velocity does it strike the earth?

 4. A plane is flying at 8 000 m. If a package is dropped from the plane
a) how long will it take the package to reach the ground?
b) what would be the acceleration of that package as it fell if the plane was flying horizontally at 2 E 3 m/s?
c) how far would the plane travel while the package was falling?
d) how many kilometers away from the target area would the plane have to drop the package to have it hit the target area?
e) how fast would the rock be traveling when it hit the ground?

5.  A plane is traveling at a speed of 250 m/s at an altitude of 12 000 m.
a) how far before the target must the plane drop an object to insure a hit?
b) how long will the object take to reach the ground?
c) how fast is the object traveling just before it hits the ground?
d) how fast is the object traveling when it is halfway to the ground?
e) suppose another plane dropped another object that required 18.5 s to reach the ground. What was the altitude of that plane?
f) if the second plane drops an object 11 km miles short of its target to insure a hit, how fast is the plane traveling?