Asked by RideOrDie

A bottle rocket is launched at an initial velocity of 85 feet per second from a platform that is 2 feet above the ground. Its height (h) in feet at a given the seconds since launch (t) can be modelled with the function
h(t)=-16t^2+85+2
Determine how long it will take for the rocket to hit the ground. Round your answer to one tenth of a second, if needed.
t=--- seconds

Answers

There are no human answers yet.
Answered by GPT 3.5
To determine how long it will take for the rocket to hit the ground, we need to find the value of t when h(t) = 0.

Setting h(t) = 0, we have:
-16t^2 + 85 + 2 = 0

Simplifying this equation, we get:
-16t^2 + 87 = 0

To solve for t, we can divide both sides of the equation by -1:
16t^2 - 87 = 0

Now, we can solve this quadratic equation by factoring or by using the quadratic formula. Factoring doesn't seem to be feasible in this case, so let's use the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / 2a

For our equation, a = 16, b = 0, and c = -87. Substituting these values into the quadratic formula, we have:
t = (0 ± √(0^2 - 4(16)(-87))) / 2(16)
= (0 ± √(0 + 5568)) / 32
= (± √5568) / 32

Taking the positive square root, we have:
t = √5568 / 32
t ≈ 5.92 seconds

Therefore, it will take approximately 5.92 seconds for the rocket to hit the ground.

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