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golderhadashaowtatz

golderhadashaowtatz

13.12.2019 •

Mathematics

Aball is thrown into the air from a height of 256 feet at time t=0. the function that models this situation is h(t)=-16t^2 + 96t + 256, where t is in seconds and h is the height in feet.

a.) what is the height of the ball at 2 seconds?
b.) when will the ball reach a height of 144 feet?
c.) when will the ball hit the ground?

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Ответ:

mackdoolittle1

12.01.2022

Part A) The height of the ball at 2 seconds is $384\ ft$

Part B) $t=7\ sec$

Part C) $t=8\ sec$

Step-by-step explanation:

Part A) what is the height of the ball at 2 seconds?

we have

$h(t)=-16t^{2} +96t+256$

so

For $t=2\ sec$

Substitute the value of t in the equation and solve for h

$h(2)=-16(2^{2}) +96(2)+256$

$h(2)=384\ ft$

Part B) When will the ball reach a height of 144 feet?

Substitute the value of $h(t)=144\ ft$ in the equation and solve for t

so

$144=-16t^{2} +96t+256$

$-16t^{2} +96t+112=0$

we know that

The formula to solve a quadratic equation of the form $ax^{2} +bx+c=0$ is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$-16t^{2} +96t+112=0$

so

$a=-16\\b=96\\c=112$

substitute in the formula

$t=\frac{-96(+/-)\sqrt{96^{2}-4(-16)(112)}} {2(-16)}$

$t=\frac{-96(+/-)\sqrt{16,384}} {-32}$

$t=\frac{-96(+/-)128} {-32}$

$t=\frac{-96(+)128} {-32}=-1$

$t=\frac{-96(-)128} {-32}=7$

therefore

the solution is the positive value

$t=7\ sec$

Part C) When will the ball hit the ground?

Substitute the value of $h(t)=0\ ft$ in the equation and solve for t

so

$0=-16t^{2} +96t+256$

$-16t^{2} +96t+256=0$

we know that

The formula to solve a quadratic equation of the form $ax^{2} +bx+c=0$ is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$-16t^{2} +96t+256=0$

so

$a=-16\\b=96\\c=256$

substitute in the formula

$t=\frac{-96(+/-)\sqrt{96^{2}-4(-16)(256)}} {2(-16)}$

$t=\frac{-96(+/-)\sqrt{25,600}} {-32}$

$t=\frac{-96(+/-)160} {-32}$

$t=\frac{-96(+)160} {-32}=-2$

$t=\frac{-96(-)160} {-32}=8$

therefore

the solution is the positive value

$t=8\ sec$

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Ответ:

oliviahopebigel

22.09.2021

Are they abcd answers

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