Problem
The distance an object falls in t seconds is given by the formula
where g is the force of gravity. If a penny is dropped from the top of the Empire State Building (350 meters tall), what is its average velocity? What is its average velocity on the [340 meters, 350 meters], that is, during its final 10 meters before it hits the ground?
Solution
We first find the time tf it takes the penny to fall from the top of the building to the ground. The equation we need to solve for tf is
The force of gravity is
Substitute this value for g and solve for tf.
To find the average velocity, use the formula
Substitute the time found above and solve for rate.
To find the average velocity over the last 10 meters, we need to figure out how much time it takes to cover those last 10 meters. We know, from the first part of this problem, that it will take about 8.45 seconds to reach the ground. We use a similar technique to find out how long it will take to fall 340 meters.
Therefore, it takes the penny
to fall the final 10 meters, with an average velocity of
