Question

the table relates to a function h(t) that models the height of a ball t seconds after it is dropped.
determine the initial height of the ball and the time interval before the ball hits the ground.
initial height = 150, hits the ground between 4 and 5 seconds
initial height = 0, hits the ground between 3 and 4 seconds
initial height = 150, hits the ground between 5 and 6 seconds
initial height = 0, hits the ground between 5 and 6 seconds

Explanation:

Step1: Identify initial height

The height of the ball at time $t = 0$ is the initial height. From the table, when $t=0$, $h(0)=150$.

Step2: Determine when the ball hits the ground

The ball hits the ground when $h(t)<0$. Looking at the table, $h(5) = 27.5$ and $h(6)= - 26.4$. So the ball hits the ground between 5 and 6 seconds.

Answer:

initial height = 150, hits the ground between 5 and 6 seconds