Question

A rocket is launched straight up from the top of a 24 foot tall building with an initial speed of 92 feet per second. the height of the rocket as a function of time can be modeled by the function h(t)= 16t²92t 24. how long will it take for the rocket to hit the ground?

O t=6 seconds
O T=7 seconds
O T=5 seconds
O T=3

Answer 1

-4.84

Step-by-step explanation:

To determine how long it will take for the rocket to hit the ground, we need to find the time at which the height of the rocket, represented by the function h(t) = 16t² + 92t + 24, equals zero.

Setting h(t) equal to zero, we have:

16t² + 92t + 24 = 0

To solve this quadratic equation, we can use the quadratic formula:

t = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 16, b = 92, and c = 24. Plugging these values into the quadratic formula, we get:

t = (-92 ± √(92² - 4 * 16 * 24)) / (2 * 16)

Simplifying further:

t = (-92 ± √(8464 - 1536)) / 32

t = (-92 ± √6928) / 32

Calculating the square root of 6928, we get:

t = (-92 ± 83.24) / 32

Now, we have two possible solutions:

t₁ = (-92 + 83.24) / 32

-0.27

t₂ = (-92 - 83.24) / 32

-4.84

Since time cannot be negative in this context, we discard the negative solution. Therefore, the rocket will hit the ground approximately 4.84 seconds after it was launched.

Please note that the provided answer is an approximation and may vary slightly depending on the level of precision required.

Answer 2

The rocket will hit the ground at t = -1 seconds.

Step-by-step explanation:

To find the time it will take for the rocket to hit the ground, we need to determine the value of t when the height h(t) is equal to zero.

The function representing the height of the rocket as a function of time is h(t) = 16t^2 + 92t + 24.

Setting h(t) = 0 and solving the quadratic equation, we get:

16t^2 + 92t + 24 = 0

Using factoring or the quadratic formula, we find that the two solutions are t = -1.5 and t = -1.

Since time cannot be negative, we ignore the solution t = -1.5.

Therefore, the rocket will hit the ground at t = -1 seconds.