Question

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?

Answer 1

Please see the explanation for steps leading to the answer:
`t ~~ 1.19" s"`

Explanation:

Set h = 1 and the solve for t:

`1 = -4.9t^2 - 5t + 2`

`-4.9t^2 - 5t + 1 =`

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

`t = {5 + sqrt((-5)^2 -4(-4.9)(1))}/(2(4.9))`

`t = {5 + sqrt((-5)^2 -4(-4.9)(1))}/(2(4.9))`

`t ~~ 1.19" s"`