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

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.

 0.72 

0.65 

0.35 

0.27

Answer 1

Probably .72 is the answer, but

depends on the problem, was initial velocity really 36 or just 6? IF 36, none of the answers are close.

set h=0 and solve for t

-16t^2 +36t + 4 = 0

this must be a typo, as 36 fits this equation, not 6. the middle term is Vot where Vo = initial velocity

now divide by -4

4t^2 -9t -1 = 0

solve for t, either factor, complete the square or use the quadratic formula

t = 9/8 + or - (1/8)sqr(81+16) = 9/8 + or - (1/8)sqr97 = 9/8 + or - (1/8)(9.85) = 1.125 + or - 1.15 = 2.275 seconds, ignore the negative solution.

but that doesn't fit any answer, so the "36" was the mistake, and the initial velocity was just 6

-16t^2 + 6t + 4 = 0 (-16 is gravity, 6 is initial velocity, 4 is initial height)

divide by -2

8t^2 - 3t - 2 = 0

t = 3/16 + or - (1/16)sqr(9+64) = 3/16 + or - (1/16)sqr(73) = 3/16 + or - 0.534 = 0.7215 which is closest to and rounded is .72. ignore the negative time solution

It's about 1/4 second = 0.25 seconds, plug that into the equation

-16(1/4)^2 + 6(1/4) + 4

=-1 +1.5 + 4 = 4.5 which does not equal zero

try 3/4

-16(3/4)^2 +6(3/4) + 4 =

-9 + 9/2 +4 = 1/2, that's close to zero

.72 is probably the answer

otherwise try 1/3 or 2/3 which are close to the 2nd and 3rd answers

-16(1/3)^2 = -16/9 + 6/9 + 4 = -10/9 + 4 = closer to 3

try 2/3

-16(2/3)^2 = - 64/9 + 4 +4 = 72/9-64/9 = 8/9 = .8888....

It's either .72 or .65, .75 gives h= .5 which is closer to zero than .888

Go with .72

Answer 2

Solve the quadratic equation h(t)=0 for t.