Final answer:
To find the ball's velocity at 96 feet, solve the height equation s(t) = 96 for time 't' and then use the velocity function v(t) = 80 - 32t to calculate the velocity at that time.
Step-by-step explanation:
To determine the velocity of the ball when it is 96 feet above the ground on its upward path, we first need to find the time at which the ball reaches this height. Using the given height function, s(t) = 80t - 16t2, set s(t) equal to 96 feet:
96 = 80t - 16t2
We can solve this quadratic equation to find the time 't'. After finding the time, we can calculate the velocity at that specific time using the derivative of the height function, which gives us the velocity function v(t) = s'(t) = 80 - 32t. Finally, plug in the time 't' when the height is 96 feet into the velocity function to find the velocity of the ball.