Problema Solution
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 provided by our tutors
h = -16 t^2 + vt + s,
v = 45 ft/s
s = 2.5 ft
t = the time in seconds
h = the heights in feet
the equation to model the height h in feet of the ball t seconds after it has been punted is
h = - 16t^2 + 45t + 2.5
The football is caught at 5.5 feet above the ground meaning we need to find t when h = 5.5 that is
- 16t^2 + 45t + 2.5 = 5.5
by solving we find two solutions
t1 = 0.068 s
t2 = 2.744 s
click here to see the step by step solution of the quadratic equation
the height of the ball is 5.5 ft above the ground after 0.068 seconds and 2.744 seconds, thus in the first solution the football was in the air 0.068 seconds and for the second solution the football was in the air 2.744 seconds.