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A ball is thrown directly upward from a height of 5 ft with an initial velocity of 24 ft/sec. The function s(t) = -16t^2+24t+5 gives the height of the ball, in feet, t seconds after it has been thrown. Determine the time at which the ball reaches its maximum height and find the maximum height.​

Sagot :

Answer:

The maximum height is 14 feet and it will take 0.75 s to reach there.

Step-by-step explanation:

A ball is thrown directly upward from a height of 5 ft with an initial velocity of 24 ft/sec.

The function is :

[tex]s(t) = -16t^2+24t+5[/tex] ....(1)

It gives the height of the ball, in feet, t seconds after it has been thrown.

For maximum height,

s'(t) = 0

So,

-32t+24 = 0

t = 0.75 s

It will take 0.75 s to reach the maximum height.

Put t = 0.75 s in equation (1). So,

[tex]s(0.75) = -16(0.75)^2+24(0.75)+5\\\\s=14\ feet[/tex]

So, the maximum height is 14 feet and it will take 0.75 s to reach there.

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