Question

a soccer player kicks a ball. the height of the ball, h(t) in feet, t seconds after it is kicked, is given by h(t)= -16t^2+45t+5. what is the ball at a height of 16 feet and how long will it take for the ball to hit the ground?

Answer 1

do you mean "when" is the ball....

Answer 2

that is how it is written thats why i wrote it like that

Answer 3

Assuming "when" is meant, you need to substitute 16 for h(t) and solve to find t.\[16=-16t ^{2}+45t+5\]

Answer 4

i forgot how to solve it when i have to substitute a number

Answer 5

Rearrange like this to form a quadratic:\[16t ^{2}-45t+11=0\]
Then use the formula for the roots of a quadratic:
\[Roots=\frac{-b \pm \sqrt{(b ^{2}}-4ac)}{2a}\]

Answer 6

\[\frac{45\pm \sqrt{1321}}{32}\]
Can you calculate them?

Answer 7

yeah

Answer 8

after that what else am i suppose to do

Answer 9

Select the appropriate root which is the time in seconds for the ball to reach a height of 16 feet. Can you do that and post back the result here for checking?

Answer 10

Then you put h(t) equal to zero and solve for t to find how long it will take for the ball to hit the ground.

Answer 11

no i cannot do that part

Answer 12

the final answers you should get are 2.54 and 0.27

Answer 13

yeah i know that those are the answers i need but cant seem to get them

Answer 14

What do you get when you calculate the roots as above?

Answer 15

to be honest nothing. im completely lost

Answer 16

you add 45 to the root of 1321 then divide the answer by 32. once you have the answer to that you then get 45 and minus the root of 1321 from it and then divide the whole thing by 32. that should give you two seperate answers.

Answer 17

thanks

Answer 18

do you get it?

Answer 19

it is basically a parabola and you are finding the two x values which corresponds to a h value of 16 (feet)

Answer 20

yes i get it know.. thanks it was a big help.

Answer 21

no probs

Answer 22

but to find out the seconds for how long it will take the ball to hit the ground. how do i find that out?

Answer 23

now instead of 'h' being 16 let it be 0 feet. and go through the same processas before

Answer 24

ok thanks so much

Answer 25

no probs

Answer 26

got lost again can u help

Answer 27

sure with the last question?

Answer 28

yes with the last question

Answer 29

ok so you use the quadratic formula as seen previously in this post.. just plug the numbers in . you get two answers and one is negative and the other is positive. since you cannot have a negative time value then it must be the positive one which works out to be 2.92

Answer 30

i dont get that answer

Answer 31

Roots=−b±(b 2 − − − √ −4ac) 2a ... plug in the co efficients according to this equation

Answer 32

or the equaation which kropot72 posted