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During the half time of a basketball game, a sling shot launches T-shirts at the crowd. The T-shirt is launched with an initial upward velocity of 60 ft/s from a height of 5 feet.

Use f(x) = -12x^2 + 60x + 5 to help you answer the following questions,

a. How long will it take for the T-shirt to reach maximum height?

b. What is the maximum height ?

1 Answer

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Explanation:

The T-shirt is launched with an initial upward velocity of 60 ft/s from a height of 5 feet. Its equation of motion is given by :


f(x) = -12x^2 + 60x + 5 ....(1)

(a) For maximum height, put
(df(x))/(dt)=0

So,


( d(-12x^2 + 60x + 5))/(dt)=-24x+60

Now put,


-24x+60=0\\\\x=2.5\ s

So, the time taken for the T-shirt to reach maximum height is 2.5 seconds.

(b) Put x = 2.5 s in equation (1)


f(x=2.5) = -12(2.5)^2 + 60(2.5) + 5\\\\f(x)=80\ \text{feet}

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