During halftime of a basketball game, a sling shot lauches T-shirt is launched from a height of 6 feet with an initial upward velocity of 80 feet per second. The T-Shirt is caught 48 feet above the

Question

During halftime of a basketball game, a sling shot launches T-shirt is launched from a height of 6 feet with an initial upward velocity of 80 feet per second. The T-Shirt is caught 48 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 + 80t + 6 = height at time t

h'(t) =-32t+80 =0

t=80/32 = 5/2 = 2.5 seconds to reach max height

h(2.5) = -16(5/2)^2 + 80(5/2) + 6 = -100+200+6=106 ft = max height

h(t)=0 = -16t^2 + 80t + 6

8t^2 -40t -3 = 0

t= 40/16 + (1/16)sqr(1600+96) = 2.5+2.57 = 5.07 seconds to reach the floor

domain is t= 0 to about 5.07 seconds

range is h=6 to 106 feet