I had a student ask a question I cant seem to find the answer.

If they dropped a 1lb object from 40,000 feet in the air, at what speed would it it the ground?

If you can help, I would appreciate it.

thank You.

HI Robert,

The usual assumption for this type of problem is that it happens in a vacuum, that is that you can ignore air resistance. In this case you can use the Newtonian fact that the force of gravity is a constant (32 feet per second per second) to develop expressions for the velocity and distance travelled. If your student is a calculus student then he/she should be able to develop these expressions using antidifferentiation. The expressions are:

s = s0 + v0t + (1/2) a t2
v = v0 + at

where s is the distance travelled in feet, s0 is the initial position, v0 is the initial velocity in feet per second, t is time in seconds and a is the acceleration in feet per second per second.

Since the object was "dropped" the initial velocity, v0 is 0. I will assume that time starts when the ball is dropped and distance is measured upward from the ground. Since "upward is positive, s0 = 40 000 feet and a = -32 feet /second2

To use the second expression to find the velocity when it hits the ground you need to know the time when it hits the ground. You can find this from the first expression since the object hits the ground when s = 0. Hence

0 = 40 000 + (1/2) (-32) t2

Solve for t to find when the object hits the ground and substitute t into the second expression to find the velocity. (The answer should be negative since distance is measured upward and the object is moving downward.)

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