Question

Natalie found a tennis ball outside a tennis court. She picked up the ball and threw it over the 12-foot fence into the court. The height of the ball, h, and time t seconds is given by the equations h(t) = -16t^2 + 18t +5. Will she make it iver the fence?

Answer 1

Natalie cannot make it over the fence.

Explanation:

After reading the statement, we must demostrate if the following inequation is possible, that is:

`-16\cdot t^(2)+18\cdot t+5 \ge 12`

After some algebraic handling we find this equivalent expression:

`16\cdot t^(2)-18\cdot t +7\le 0` (1)

The polynomial is factorized by the Quadratic Formula:

`\left(t-0.563-i\,0.348)\cdot (t-0.563+i\,0.348)\le 0`

Since all roots are complex, we conclude that Natalie cannot make it over the fence.