Suppose h(t)=-0.2t squared +2t models the height in feet of ball that is kicked into the air where t is given as time in seconds what is the maximum height in seconds. what is the maximum height the ball travels in feet. after how many seconds does the ball reach the ground in seconds.

To get the maximum height, we first determine the time at which this maximum height is attained by differentiating the given equation and equating the differential to zero. 
                                 h(t) = -0.2t² + 2t
Differentiating,
                               dh(t) = -(0.2)(2)t + 2 = 0
The value of t is equal to 5. Substituting this time to the original equation,
                                   h(t) = -0.2(5²) + 2(5) = 5 ft
Thus, the maximum height is 5 ft and since it will take 5 seconds for it to reach the maximum height, the total time for it to reach the ground is 10 seconds. 

Answers: maximum height = 5 ft 
                  time it will reach the ground = 10 s

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