Answer:
Step-by-step explanation:
Assuming the ball leaves the ground at a height, h = 0 ft, then the equation for the height is given by:
h = 96t - (1/2)(32)t² = 96t - 16t²
To determine the maximum height, find dh/dt, set it equal to zero, and solve for "h":
dh/dt = 96 - 32t = 0
t = 96/32 = 3 seconds (this is the time it takes for the ball to reach maximum height)
Substitute t = 3 into the original equation and solve for "h":
h(3) = 96(3) - 16(3)² = 288 - 144 = 144 feet
