Question

If a football player passes a football from 4 feet off the ground with an initial velocity of 36 feet per second, how long will it take the football to hit the ground? Use the equation h = −16t2 + 6t + 4. Round your answer to the nearest hundredth.
A)0.72
B) 0.65
C)0.35
D)0.27

Answer 1

Option A: The football will take 0.72 seconds to hit the ground.

Explanation:

Given that the equation is $h=-16 t^{2}+6 t+4$

We need to determine how long will it take the football to hit the ground.

Let us substitute h = 0 in the above equation.

Thus, we have,

$0=-16 t^{2}+6 t+4$

Now, we shall simplifying the equation using the quadratic formula.

The formula is given by

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Substituting the values $a=-16, b=6, c=4$ in the above formula, we get,

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

Simplifying, we get,

$t=\frac{-6 \pm \sqrt{36+256}}{-32}$

$t=\frac{-6 \pm \sqrt{292}}{-32}$

$t=\frac{-6 \pm 2\sqrt{73}}{-32}$

Taking out 2 as a common term, we get,

$t=-\frac{2(-3 \pm \sqrt{73})}{32}$

Dividing, we get,

$t=-\frac{-3 \pm \sqrt{73}}{16}$

Thus, the roots of the equation are $t=-\frac{-3+\sqrt{73}}{16}, t=\frac{3+\sqrt{73}}{16}$

Simplifying the roots of the equation, we have,

$t=-0.35$ and $t=0.72$

Since, t cannot take a negative value, we have,

$t=0.72$

Therefore, the football will take 0.72 seconds to hit the ground.

Hence, Option A is the correct answer.