Question

4. A ball is thrown straight up at an initial

velocity of 54 feet per second. The height
of the ball t seconds after it is thrown is
given by the formula h(t) = - 12ť + 54t.
How many seconds after the ball is thrown
will it return to the ground?

Answer 1

`t = (9)/(2)\,s`

Explanation:

The time required by the ball to return to the ground is determined by equalizing height to zero:

`h(t) = -12\cdot t^(2) + 54\cdot t`

`-12\cdot t^(2) + 54\cdot t = 0`

`-6\cdot t \cdot (2\cdot t -9) = 0`

Roots are described below:

`t_(1) = 0\,s`

`t_(2) = (9)/(2)\,s`

The second one corresponds to the time when the ball is returning to the ground.