Question

A baseball is thrown into the air from the top of a 224-foot tall building. The baseball's approximate height over time can be represented by the quadratic equation h(t) = -16t2 + 80t + 224, where t represents the time in seconds that the baseball has been in the air and h(t) represents the baseball's height in feet. When factored, this equation is h(t) = -16(t - 7)(t + 2).

What is a reasonable time for it to take the baseball to land on the ground?

A.
5 seconds
B.
9 seconds
C.
2 seconds
D.
7 seconds

Answer 1

D. 7s

Explanation:

h(t) = height off the ground

We know the height of the ball at the point when it hits the ground will be 0, so we set h(t) = 0:

h(t) = -16(t - 7)(t + 2) = 0

In order for this to be true, either:

"t - 7 = 0" or "t + 2 = 0"

We can solve these to get the times at which the ball will hit the ground, which gives:

t = 7 or t = -2

-2s is not a logical time because the ball can't hit the ground before it is thrown so this solution is not relevant;

7s therefore is the correct solution