Algebra math project

Question

A ball is thrown into the air with an upward velocity of 44 ft/s. It's height h in feet after t seconds is given by the function h=-16t²+44t+10. How long does it take the ball to reach its maximum height? What is the maximum height?

Answer 1

a.) How long does it take the ball to reach its maximum height?

For an equation h(t)=-at²+bt+c, the maximum height can be found at the point t=-b/2a. Here -b=44 and a=-16. Plug in these two numbers and simplify. Doing so:

t=-44/2*(-16)

t=22/16

t=11/8

b.) What is the maximum height?

Plug the t-value we calculated above into the original equation

h=-16*(11/8)^2+44*11/8+10

h=-30.25+60.5+10

h=40.25=161/4