How long will it take the t-shirt to reach its maximum height? What is the maximum height? What is the range of the function that models the height of the T shi

Question

During halftime of a basketball game, a sling shot launches t- shirts at the crowd. A t-shirt is launched from a height of 5 feet with an initial upward velocity of 88 feet per second. The t-shirt is caught 39 feet above the court. How long will it take the t-shirt to reach its maximum height? What is the maximum height? What is the range of the function that models the height of the T shirt over time?

Answer 1

h(t) = -16t^2 + 88t + 5

max height is reached when the derivative = 0

h'(t) =-32t + 88 = 0

t= 88/32 = 11/4 = 2 3/4 seconds

max height = h(11/4) =-16(11/4)^2 + 88(11/4) + 5 = -121+242+5 = 126 feet

if they're caught at 39 feet, the range is 5 to 39 feet