Question

When a person throws a ball into the​ air, it follows a parabolic path that opens downward as shown in the figure to the right. Suppose that the​ ball's height in feet after t seconds is given by ​h(t)=-16t^2+32t+2. If​ possible, determine the​ time(s) when the ball was at a height of 14 feet.

Answer 1

0.5 seconds and 1.5 seconds.

Explanation:

h(t) = -16t^2 + 32t + 2

14 = -16t^2 + 32t + 2

16t^2 - 32t - 2 + 14 = 0

16t^2 - 32t + 12 = 0

8t^2 - 16t + 6 = 0

4t^2 - 8t + 3 = 0

(2x - 3)(2x - 1) = 0

2x - 3 = 0

2x = 3

x = 3/2

x = 1.5

2x - 1 = 0

2x = 1

x = 1/2

x = 0.5

So, the ball was at 14 feet at 0.5 seconds and 1.5 seconds.

Hope this helps!