Question

Suppose h(t) = -0.2t? + 2t models the height, in feet, of a ball that is kicked into the air where t is

given as time, in seconds.
After how many seconds does the ball reach its maximum height?
seconds
What is the maximum height of the ball?
After how many seconds does the ball reach the ground?
seconds

Answer 1

Below in BOLD.

Explanation:

h(t) = -0.2t^2 + 2t

We can find the maximum height and the time by converting to vertex form:

h(t) = -0.2(t^2 - 2t)

= -0.2[(t - 1)^2 - 1)

= -0.2(t - 1)^2 + 0.2

The time to get to maximum height = 1 second and the maximum height is 0.2 m.

When the ball reaches the ground h = 0 so

-0.2(t - 1)^2 + 0.2 = 0

(t - 1)^2 = -0.2 / -0.2 = 1

t - 1 = 1

t = 2 seconds.