Question

Due to gravity, an object falls 16t^2 feet in t seconds. You drop a backpack from a window that is 20 feet above the ground. Will the backpack hit the ground in 1 second?

Answer 1

NO

Explanation:

Let h(t) represent the distance the pack is located above the ground at time t. Then h(t) = 20 ft - 16t^2 ft. Notice how h = 20 ft (the initial height) and that it decreases as t increases.

How long does it take for the pack tohit the ground? Set h(t) = 0 and solve for t:

0 ft = 20 ft - 16t^2 ft yields 16t^2 ft = 20, or t^2 ft = 20/16, which is greater than 1. So the question "Will the backpack hit the ground in 1 second" is answered by NO.