Example 3: When a football is kicked with a vertical speed of 20m/s, its height,

*h* metres, after

*t* seconds is given by the formula:

How long after the kick is the football at a height of 15m?

Solution

Substitute 15 for

*h* in the formula:

This produces a quadratic equation. The solution of the equation gives the times when the height is 15m.

Collect all the terms on one side of the equation.

Either

or

The football is at a height of 15m twice: first on the way up, 1 s after the kick, then on the way down, 3 s after the kick.