Quadratic Equations

Question

when a football is kicked with a vertical speed of 20m/s, it's height, h meters, after t seconds is approximated by the formula: h = 20t - 5t^2. How long after the kick is the football at the height of 15m?

Answer 1

Since we know h = 15 m, we can plug that value in to the equation and solve for t:

15 = 20t - 5t² Let's set the equation equal to 0 to solve

-5t² + 20t - 15 = 0 Let's factor out a -5 to simplify the equation

-5(t² - 4t + 3) = 0 0/-5 is still 0

t² - 4t + 3 = 0 Let's find factors for this solution

(t -3)(t - 1) = 0 We have 2 solutions for this equation

t = 3, t = 1