Problema Solution
The height h in feet of a ball after 1 seconds is given by h = 48t-16t^2. How long did it take for the ball to hit the ground?
Answer provided by our tutors
basically solve the equation for h=0 (the ground is when the h=0)
I will take the liberty of flipping all the signs
16t^2 - 48t = 0
(simplify by dividing by dividing by 16)
t^2 - 3t = 0
t^2 -3t = 0
(complete the square - add the square of half the coefficient of the middle term to both sides)
t^2 - 3t + 1.5^2 = 1.5^2
(factor the left side)
(t - 1.5)^2 = 9/4
take the square root of both sides
t - 1.5 = PLUS/MINUS (3/2)
t = 1.5 plus/minus 1.5
t = 3 or 0
Obviously t = 0 is when you hit the ball in the first place, so the answer you want is t=3