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 + 36t + 4.

quantity of 9 plus or minus square root of 65 all over 8

9 plus or minus square root of 65 end root over 8

quantity of 9 plus or minus square root of 97 all over 8

9 plus or minus square root of 97 end root over 8

Answer 1

You need to find time \(t\) when the ball is at height \(h(t) = 0\), i.e. solve the quadratic equation\[-16t^2+36t+4 = 0\]Can you do that?

Answer 2

Notice that there is a common factor of 4. First thing I would do is factor out the 4. Then apply the quadratic formula to get your answer.

Answer 3

is it a?

Answer 4

How did you get a?

Answer 5

sim-36+-square root of (36)^2 -4(16)(4)/2(16)

Answer 6

simplify 36/32

Answer 7

OK but then it will need to be simplified by factoring out common factors. It is easier to do this beforehand. simplify\[-16x^2+36x+4=0\]by factoring out a common factor of 4

Answer 8

Hello?

Answer 9

ok so the answer is 9 square root 65 all over 8

Answer 10

Not quite. I assume you've factored out the 4 to get\[-4x^2 + 9x + 1 = 0\]Now apply the quadratic formula with a=-4, b=9, and c=1.

Answer 11

\[x=\frac{ -9 \pm \sqrt{9^2-4(-4)(1)} }{ 2(-4) } = ?\]

Answer 12

is it the whole thing over 8?

Answer 13

-9+-square root of 97/

Answer 14

-8

Answer 15

@ospreytriple

Answer 16

Very good. Now you a negative divide by a negative. So it can be simplified a tiny bit more to get your final answer.