Problem

A meteoroid falling to Earth is discovered when it is at an altitude of 9000 kilometers, traveling at a velocity of 70 kilometers per second. Assuming acceleration due to Earth's gravity is constant, and neglecting air resistance, how fast will the meteoroid be falling when it hits the ground? What will its acceleration be?

Solution

Use the equation

to find how long it takes for the meteoroid to hit the ground.

This is a quadratic equation in the variable t, which we can solve using the quadratic formula. First convert lengths into the same unit.

t₁ is the only solution that makes sense.

Since v = v₀ + at, the velocity will be

Since the acceleration is constant throughout the fall, when the meteoroid hits the ground it will still have an acceleration of 9.8 m/sec².