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1. Omar set off a rocket in a field. The height h of the rocket in feet can be roughly estimated using the formula

h = -16t^2 + 128t, where t is the time in seconds. How long will it take the rocket to reach a height of 240 feet?


2. Josefina tosses a ball upward with an initial velocity of 76 feet per second.

She tosses it from an initial height of 2 feet. Find the approximate time that the ball hits the ground.

Use the function h(t) = -16t^2 + 76t + 2

Round to the nearest second.



3. Brandi, an amateur skier, begins on the "bunny hill," which has a vertical drop of 200 feet.

Her speed at the bottom of the hill is given by the equation v^2 = 64h, where the velocity v is in feet per second

and the height h of the hill is in feet. Assuming there is no friction, approximate Brandi's velocity at the bottom of the hill.

Respuesta :

Rodiak
1.
Height h = 240 feet
We insert it into formula.
[tex]240 = -16 t^{2} +128t[/tex]
Now we solve this for t:
[tex]16 t^{2} -128t +240 = 0 /16 \\ t^{2} - 8t +15 =0 \\ t_{1} = 5 t_{2} = 3[/tex]

We have two answers as the rocket will pass this height on it's way up and down.

2.
Height h = 0 feet
We insert it into formula.
[tex]0=-16 t^{2} +76t + 2[/tex]
Now we solve this for t:
[tex]16 t^{2} - 76t -2 = 0 /2 \\ 8t^{2} - 38t - 1 = 0 \\ t_{1} = 5 t_{2} = -1[/tex]
We do not consider solution -1 as the time can not be negative. Our solution is 5s.

3.
Height at bottom of hill h = 0 feet
We insert it into formula.
[tex] v^{2} = 64 * 0 = 0 ft/s[/tex]