Question

A model rocket is launched from the top of a building. The height (in meters) of the rocket above the ground is given by h( t) = -16t2 + 96t + 14, where t is the time (in seconds) since the rocket was launched. How long will it take for the rocket to hit the ground?

Answer 1

To determine how long it will take for the rocket to hit the ground, we need to find the time when the height of the rocket is equal to zero. In the given equation, h(t) = -16t^2 + 96t + 14.

Setting h(t) = 0, we have:

-16t^2 + 96t + 14 = 0

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

t = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = -16, b = 96, and c = 14. Plugging these values into the quadratic formula will give us the solutions for t.

Explanation: