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.

Step-by-step 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=(-6 \pm √(36+256))/(-32)`

`t=(-6 \pm √(292))/(-32)`

`t=(-6 \pm 2√(73))/(-32)`

Taking out 2 as a common term, we get,

`t=-(2(-3 \pm √(73)))/(32)`

Dividing, we get,

`t=-(-3 \pm √(73))/(16)`

Thus, the roots of the equation are
`t=-(-3+√(73))/(16), t=(3+√(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.