Question

During halftime of a football ​game, a sling shot launches​ T-shirts at the crowd. A​ 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 33 feet above the field. 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

16 = (1/2) g = 32/2

v = 80 - 32 t
v = 0 at top
so
at top t = 80/32 = 2.5 seconds upward to top

h = 6 + 80 t - (16) t^2
at top
h = 6 + 80 (2.5) - 16 * 6.25 = 6 + 200 - 100 = 106 feet at top
range is 6 feet to 106 feet

Answer 2

I think speedycake may have been doing a similar problem starting at 5 feet and 64 ft/s.