A rock is thrown into the air. The height of the rock is modeled by s(t) = −16tଶ + 64t + 80 feet for t ≥ 0 seconds. The rock hits the ground at t = 5 seconds. Find the maximum height of the rock on the interval 0 ≤ t ≤ 5.

144 feets

Step-by-step explanation:

Look on s(t) like quadratic function. We need to find maximum of the function using 1st diferetioal:

s(t)=-16t^2+64t+80

s’(t)=-32t+64

S’(t)=0 if t=2

For t>2, s’(t)<0

For t<2, s’(t)>0. So the maximum od function is in the point 2.

S(2)=-16*4+64*2+80=-64+128+80=144

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