Question

A football is punted from a height of 2.5 feet above the ground with an initial vertical velocity of 45 feet per second. Write an equation to model the height h in feet of the ball t seconds after it has been punted. The football is caught at 5.5 feet above the ground. How long was the football in the air?

Answer 1

First assume that the football is going straight up, that is important.  next you have a good rate problem here.  So you have y = mx + b, where m is the rate and b is the starting point.  Now plug in data m is 45 ft/s and b = 2.5ft, so the equation is y = 45x + 2.5.  Now the ball was caught at 5.5 so put that in for y.  5.5 = 45x + 2.5.  Solve to get 1/9 of a sec.