# A soccer player kicks the ball to a height of 1 meter inside the goal. The equation for the height h of the ball at time t is h=-4.9t^2-5t+2, how do you find the time the ball reached the goal?

Nov 9, 2016

$t \approx 1.19 \text{ s}$

#### Explanation:

Set h = 1 and the solve for t:

$1 = - 4.9 {t}^{2} - 5 t + 2$

$- 4.9 {t}^{2} - 5 t + 1 =$

Use the quadratic formula but discard the negative value, because negative time makes no sense:

$t = \frac{5 + \sqrt{{\left(- 5\right)}^{2} - 4 \left(- 4.9\right) \left(1\right)}}{2 \left(4.9\right)}$

$t = \frac{5 + \sqrt{{\left(- 5\right)}^{2} - 4 \left(- 4.9\right) \left(1\right)}}{2 \left(4.9\right)}$

$t \approx 1.19 \text{ s}$