Question

an object is thrown down from the top of a building. A height function for the object is given by the equation h=16(8+ t ) (5 - t) where T is the number of seconds elapsed since the object was thrown and H is the height of the object above the ground ( in feet). explain how to reason about the structure of the equation to determine when the object will hit the ground

Answer 1

The height is a function of the time, given by the following equation:

h(t) = 16(8+t)(5-t)

The object hits the ground when h(t) = 0. So

16(8 + t)(5 - t) = 0

This means that:

8 + t = 0 or 5 - t = 0

8 + t = 0

t = -8

We cannot have negative values for t.

5 - t = 0

-t = -5 *(-1)

t = 5

The object hits the ground when t = 5, which was easy to find since the equation was already factored by it's roots.