Question

During halftime of a soccer ​game, a sling shot launches​ T-shirts at the crowd. A​ T-shirt is launched from a height of 3 feet with an initial upward velocity of 72 feet per second. The​ T-shirt is caught 36 feet above the field.

a.) How long will it take the​ T-shirt to reach its maximum​ height?
b.) What is the maximum​ height?
c.) What is the range of the function that models the height of the​ T-shirt over​ time?

Answer 1

a. 2.1 Seconds

b. 120.6 Feet

c. 3
`\leq` y
`\leq` 120

Explanation:

The height y at time t is

y = 33 + 64t - 16t^2

The general equation that represents the height as a function of time:

f(t) = At^2 + Bt + C

f(t) = -16
`t^(2)` + 72t + 3

The maximum​ height :

t = 72/33 = 2.1sec

So, f(2.1) = -16(2.1) +72(2.1) +3 = 120.6 Feet

Therefore, 2.1 seconds will it take the​ T-shirt to reach its maximum​ height

Range of the function ,

heights ( y ) = 3
`\leq` y
`\leq` 120