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?

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letmeanswer letmeanswer · Answer 1 · 2020-03-06T11:45:40+01:00

a. 2.1 Seconds

b. 120.6 Feet

c. 3 [tex]\leq[/tex] y [tex]\leq[/tex] 120

Step-by-step 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[tex]t^{2}[/tex] + 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 [tex]\leq[/tex] y [tex]\leq[/tex] 120