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 + 36t + 4.

Question

jenniferjuice · Answer

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imstuck · Answer

Oh, good...they gave you the equation!  Some of them want you to come up with it on your own and THEN solve it too!  What you are looking to do here is to solve for t, the time it took for the football to hit the ground.  So you would factor this and solve for t.  It looks to me like you need the quadratic formula.  Do you know it?

imstuck · Answer

Solving for t, will give you the zeros of the equation, which is what you want, because you want to know how long it will take the ball to hit the ground, which is an h value of 0.

jenniferjuice · Answer

idk the formula.. .-.

imstuck · Answer

There is no way you can solve this without the quadratic formula.  I will show it to you, then maybe you will remember it when you see it.  Ok?

imstuck · Answer

$$\frac{ -b \pm \sqrt{b ^{2}-4ac} }{ 2a }$$

jenniferjuice · Answer

ok .

imstuck · Answer

So in our quadratic equation, a = -16, b = 36, c = 4.  Filling in to our formula, we get

imstuck · Answer

$$\frac{ -36\pm \sqrt{(36)^{2}-4(-16)(4)} }{ 2(-16) }$$

imstuck · Answer

That reduces to...

imstuck · Answer

$$\frac{ -36\pm \sqrt{1296+256} }{ -32 }$$Which further reduces to

imstuck · Answer

$$\frac{ 36\pm \sqrt{1552} }{ 32}$$Notice that a negative divided by a negative is a positive, so the negative signs are gone.

jenniferjuice · Answer

but then what do i dowith the square root ?

imstuck · Answer

Under the radical sign, the reduces to $$\frac{ 36\pm \sqrt{16 * 97} }{ 32 }$$And since 16 is a perfect square it comes out from under the radical as a 4:

imstuck · Answer

$$\frac{ 36\pm4\sqrt{97} }{ 32 }$$

imstuck · Answer

All of those numbers outside the radical are divisible by 4, so it further reduced to

imstuck · Answer

$$\frac{ 9\pm \sqrt{97} }{ 8 }$$And that is your answer!  It is the third choice down.

imstuck · Answer

Just for the sake of actually completing this and finding the final answer in time = seconds, you have to use this form of the answer:

imstuck · Answer

$$\frac{ 9+\sqrt{97} }{ 8 }=2.4 \sec$$because the other solution,$$\frac{ 9-\sqrt{97} }{ 8 }=-.11 \sec$$and t can never be a negative number.

imstuck · Answer

Thank you for the medal!

jenniferjuice · Answer

np!!!