Question

Yolanda throws a sphere up in the air from the top of a building. After t seconds, the height of the sphere above the ground is h feet, where h = -16t² + 30t + 78. After how many seconds does the sphere hit the ground?

Answer 1

The sphere hits the ground after 4 seconds.

Step-by-step explanation:

The equation given for the height of the sphere above the ground is h = -16t² + 30t + 78.

To find the time when the sphere hits the ground, we set the height equation equal to zero and solve for t:

-16t² + 30t + 78 = 0

By factoring or using the quadratic formula, we find two solutions: t = -5.0 s and t = 4.0 s. Since time t = 0 is when the ball is released, we are only interested in the positive root, which is t = 4.0 seconds. Therefore, the sphere hits the ground after 4 seconds.