Question

A rocket is launched from atop a 75 foot cliff with an initial vertical velocity of 107 feet per second. The height of the rocket t seconds after launch is given by the equation h = -16t + 107t + 75. Graph the equation to find out how long after the rocket is launched it will hit the ground. Estimate your answer to the nearest tenth of a second.

Answer 1

The rocket will hit the ground approximately 1.25 seconds after it is launched.

Step-by-step explanation:

To find out how long after the rocket is launched it will hit the ground, we can set the equation for the height of the rocket equal to zero and solve for t. The equation h = -16t^2 + 107t + 75 represents the height of the rocket t seconds after launch.

To solve for t, we set the equation equal to zero:

-16t^2 + 107t + 75 = 0

We can solve this quadratic equation using factoring, completing the square, or the quadratic formula. In this case, factoring is the easiest method.

The factors of -16t^2 + 107t + 75 are (4t + 15)(-4t + 5). Setting each factor equal to zero gives us:

4t + 15 = 0 --> t = -15/4
-4t + 5 = 0 --> t = 5/4

The negative value for t is extraneous, so the rocket will hit the ground approximately 1.25 seconds after it is launched.