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 4 feet with an initial upward velocity of 64 feet per second. The​ T-shirt is caught 49 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

$or$The general equation that represents height of the t-shirt as a function of time:

$64/4=16 \\f(t)= -16t^{2} +64t+5$

The maximum height of the t-shirt:

$t=\frac{-64}{2(-16)} =2\\f(2.25)=-16(2)^{2} +64(2)+5\\= 69 feet$

How long will it take the t-shirt to reach its maximum height:

2 seconds

How long does it take for the t-shirt to reach the crowd:

$49=-16t^{2} +69t+5\\o=-16t^{2}+69t-30\\\\\frac{-64+\sqrt[]{-64^{2-4(-16)(-30)}} }{2(-16)} = .54$$seconds$ or $3.04$ $seconds$

The range of this graph in  inequality and interval notation:

$heights(y)\\5\leq y\leq 69 [5,86]$