Audrey uses a slingshot to shoot a marble from a window. The height of the marble h(t) in feet at time t seconds is given by the function h(t) = -16t² - 54t + 306. How many seconds elapse before the marble hits the ground?

Question

Quizplus · Accepted Answer

To find when the marble hits the ground, we need to find when h(t) = 0.

0 = -16t^2 - 54t + 306

Simplifying by dividing both sides by -2, we get:

0 = 8t^2 + 27t - 153

Factoring or using the quadratic formula, we get:

0 = (t - 3)(8t + 51)

Therefore, the marble hits the ground at t = 3 seconds (we ignore the negative solution since time cannot be negative). So the answer is C.

Audrey Uses a Slingshot to Shoot a Marble from a Window