Question

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24. The function below model the flight of football's being kicked during a football game. ​

Answer 1

#a

Find t coordinate of vertex

• -b/2a
• -32/2(-16).
• -32/-32
• 1

Put in equation

`\\ \rm\Rrightarrow h(1)=-16+32`

`\\ \rm\Rrightarrow H_(max)=16ft`

#b

• Make h(t)=0

`\\ \rm\Rrightarrow -16t^2+32t=0`

`\\ \rm\Rrightarrow -16t(t-2)=0`

`\\ \rm\Rrightarrow t=0,2`

• At 0s and 2s the ball will be at ground

Answer 2

(a) The maximum height of the ball is 16 feet at 1 seconds.

(b) The ball hits the ground at 2 seconds.

PART (A) :

Given function: h(t) = -16t² + 32t

Comparing to quadratic function: ax² + bx + c

In this function: a = -16, b = 32, c = 0

To find the maximum height, use the vertex formula:

`\sf x = (-b)/(2a)`

Insert values

`\rightarrow \sf t = (-32)/(2(-16)) = 1`

Then find h(t) = -16(1)² + 32(1) = 16 feet

Conclusion: The maximum height of the ball is 16 feet at 1 seconds.

PART (B) :

When the ball hits the ground, the height [h(t)] will be 0 ft

-16t² + 32t = 0

-16t(t - 2) = 0

-16t = 0, t - 2 = 0

t = 0, t = 2

The ball hits the ground at 2 seconds. Note: the other 0 seconds is for when the ball was launched at the beginning.