Algebra 1 Quadratics Problem [Read Description]

Question

During halftime of a football ​game, a slingshot launches​ T-shirts at the crowd. A​ T-shirt is launched from a height of 6 feet with an initial upward velocity of 72 feet per second. The​ T-shirt is caught 48 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

max height = 87 feet

achieved in 2 1/4 or 2.25 seconds

range must be 0 to 87 feet?

not sure why 48 feet is in the problem? other than maybe to calculate when a fan catches a shirt?

h(t) = -16t^2 + 72t + 6

take the derivative and set equal to zero and solve for t

-32t +72 =0

t = 2.25

plug that into h(t) to get 87 for max height

to get the time when a fan catches a shirt set h(t) = 48

and solve for t

48=-16t^2 + 72t+ 6

do a quadratic formula, but know the solution is greater than 2.25 seconds