Question

A ball is kicked into the air from the ground. The height of the ball, h(t), in feet, after t seconds can be represented by the function h of t equals negative 16 t squared plus 96 t. What is the total amount of time the ball will be in the air? The ball will be in the air for _________ seconds.

Answer 1

Answer:

6 seconds

Step-by-step explanation:

To find the answer, we'll need to find the x-intercepts and choose the one with the higher value cause that's when the ball falls to the ground. To find the x-intercepts, we have to set the y value, h(t), to 0. When we do that, we have: -16$t^{2}$ + 96t = 0. No all we have to do is factor to find t. When factored, it becomes -16t (t-6) = 0. Now, set each of the factors to 0, and we have t = 0 or t = 6. Since 6 is the larger one, the ball will be in the air for 6 seconds.