Question

Henry throws a tennis ball over his house. The ball is 6 feet above the ground when he lets it go. The quadratic function that models the height, in feet, of the ball after t seconds is h = -16^2 + 46t + 6. Using the quadratic formula to solve, at what time does the ball hit the ground?
Please show all work and now just the answer.

Answer 1

Option C: It takes 3 seconds for the ball to hit the ground.

Explanation:

The given quadratic function is $h=-16 t^{2}+46 t+6$ where h is the height in feet and t is the time in seconds.

We need to determine at what time the ball will hit the ground.

Time taken:

The time can be determined by substituting h = 0 in the function $h=-16 t^{2}+46 t+6$

Thus, we get;

$0=-16 t^{2}+46 t+6$

Let us solve the quadratic expression using the quadratic formula.

Thus, we have;

$t=\frac{-46 \pm \sqrt{46^{2}-4(-16) 6}}{2(-16)}$

Solving, we get,

$t=\frac{-46 \pm \sqrt{2116+384}}{-32}$

$t=\frac{-46 \pm \sqrt{2500}}{-32}$

$t=\frac{-46 \pm 50}{-32}$

Thus, the values of t are given by

$t=\frac{-46 + 50}{-32}$ and $t=\frac{-46 - 50}{-32}$

$t=\frac{4}{-32}$ and $t=\frac{-96}{-32}$

$t=-\frac{1}{8}$ and $t=3$

Since, t cannot take negative values.

Thus, the value of t is $t=3$

Hence, the time taken by the ball to hit the ground is 3 seconds.

Therefore, Option C is the correct answer.