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Sam kicks a ball off of a rooftop. After t seconds, its height, h (in feet), is given by the formula: h (t) = -16t^2 + 64t + 80.

*NOTE: Complete this without using graphing features on your calculator, and show all work for credit.
a. What is the maximum height reached by the ball?

b. When did the ball reach its maximum height?

c. When will the ball hit the ground? (Do algebraically)

d. What is the height of the ball after 1 second?
EXPLAIN ALL 4 PARTS IN DEPTH, PLEASE!

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Answer:

a. 144m

b. After 2 secs

c. Ball hits the ground after 5 secs.

d. 128m

Step-by-step explanation:

A To find max height, find derivative of equation, let it equal zero, and sub in value into original equation: h(t) = -16t² + 64t + 80 h'(t)=-32t+64 -32t+64=0 32t=64 t=2 h(2) = -16(2²) + 64(2) + 80 h(2) = -64+128+80 = 144m B When h=144, t=2. Therefore, the ball reaches its max height after 2 secs. C When the ball hits the ground, h=0: -16t² + 64t + 80=0 t²-4t-5=0 (simplified) (t-5)(t+1)=0 t=5 and t=-1 Discount t=-1 (time cant be neg). Ball hits the ground after 5 secs. D Find h when t=1: h(t) = -16t² + 64t + 80 h(1) = -16(1²) + 64(1) + 80 h(1) = -16+64+80 h(1) = 128m.

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