functions are crazy

Question

Th height h (in feet) above the ground of a golf ball depends on the time, (in seconds) it has been in the air. Ed hits a shot off of the tee that has a height modeled by the function f(t)=-16t^2+80t. What is the height of the ball at 3.5 seconds? At approximately what time is the ball 65 feet in the air? Explain

Answer 1

f(t) = -16t²+80t

 

at 3.5 seconds

f(3.5) = -16(3.5)²  + 80(3.5)

f(3.5) = -196 + 280 = 84 

at 3.5 seconds, the height of the ball is 84 feet

 

The ball is 65 feet in the air when f(t) = 65

65 = -16t² +80t

Moving all terms to one side and we can rewrite this as

16t²-80t+65=0

We need to use the quadratic to solve this and we get

10±√35

--------- = 3.97 and 1.02 seconds

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