A model rocket is launched with an initial velocity of 160 ft/s. The height, h, in feet, of the rocket t seconds after the launch is given by

h = −16t2 + 160t.
How many seconds after launch will the rocket be 350 ft above the ground? Round to the nearest hundredth of a second.

-16t^2 + 160t = 350

just use the quadratic formula to solve for t.

To find the number of seconds after launch when the rocket will be 350 ft above the ground, we can set the equation h = 350 and solve for t.

Given equation: h = -16t^2 + 160t
Substituting h = 350:
350 = -16t^2 + 160t

Now we need to solve this quadratic equation. Rearranging it to standard form:
16t^2 - 160t + 350 = 0

We can solve this equation using the quadratic formula: t = (-b ± √(b^2 - 4ac)) / (2a)

For this equation, a = 16, b = -160, and c = 350. We can substitute these values into the formula and simplify:

t = (-(-160) ± √((-160)^2 - 4(16)(350))) / (2(16))
t = (160 ± √(25600 - 22400)) / 32
t = (160 ± √3200) / 32
t = (160 ± 56.57) / 32

Now we have two possible solutions for t:
t1 = (160 + 56.57) / 32 ≈ 7.31 seconds
t2 = (160 - 56.57) / 32 ≈ 2.48 seconds

Therefore, the rocket will be 350 ft above the ground approximately 2.48 and 7.31 seconds after launch, rounded to the nearest hundredth of a second.

To find the number of seconds it takes for the rocket to be 350 ft above the ground, you need to solve the equation h = 350 for t.

Given:
h = −16t^2 + 160t
h = 350

Substituting 350 for h in the equation, we have:
350 = -16t^2 + 160t

Rearranging the equation to get it in quadratic form:
16t^2 - 160t + 350 = 0

To solve this quadratic equation, you can use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / 2a

In this case:
a = 16
b = -160
c = 350

Substituting these values into the quadratic formula, we have:
t = (-(-160) ± √((-160)^2 - 4(16)(350))) / (2(16))

Simplifying further:
t = (160 ± √(25600 - 22400)) / 32
t = (160 ± √3200) / 32
t = (160 ± 56.57) / 32

Now, we have two possible solutions for t:
t1 = (160 + 56.57) / 32 = 7.69 seconds
t2 = (160 - 56.57) / 32 = 2.18 seconds

So, the rocket will be 350 ft above the ground approximately 7.69 seconds and 2.18 seconds after launch.