Question

The height of a small rock falling from the top of a 124-ft-tall building with an initial downward velocity of -30 ft/sec is modeled by

the equation h(t) = -16% - 30t + 124, where t is the time in seconds. For which interval of time does the rock remain in the air?

O

t = 2

-2
0
t> 2

Answer 1

Yo itś C

Explanation:

:-)

Answer 2

For the time interval 0 to 2 the ball is in the air.

Select the options according to this.

Explanation:

The equation should be
`h(t)=-16t^(2) -30t+124`

Let's find the x intercepts to answer this question.

To find x intercept where the h(t) is 0.

`-16t^(2) -30t+124=0`

Solve the equation for t.

Use quadratic formula to solve the equation.

a=-16

b=-30

c=124

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

Plug in the values of a, b and c into the formula

`x=\frac{30+/-\sqrt{(-30)^(2)-4(-16)(124) } }{2(-16)}`

Simplify it

`x=(30+/- √(900+7936) )/(-32)`

`x=(30+/-√(8836) )/(-32)`

`x=(30+/-94)/(-32)`

Simplify it to get two values for x

`x=(30+94)/(-32) =-3.875\\\\x=(30-94)/(-32) =2`

x can not be negative, here x represents time t.

So, it starts from 0 and remains in the air for 2 seconds.