Question

A punter kicks a football upward with an initial speed of 48 feet per second. After how many seconds does the ball hit the ground? Use the formula h = rt - 16t^2 where h represents height in feet and r represents the initial speed.

Answer 1

@rebeccaskell94

Answer 2

when it hits the ground, what will h equal?

Answer 3

0?

Answer 4

correct, so you need to solve:\[0=rt-16t^2\]

Answer 5

and you are given r=48

Answer 6

so 0 = 48t - 16t^2?

Answer 7

correct - now factorise this and the answer should become clear

Answer 8

how do i factorize this one i've always been bad at factoring :l

Answer 9

ok - look at each part.
first lets concentrate on just the numbers 48 and 16 - what is common between 48 and 16?

Answer 10

what divides into both 48 and 16

Answer 11

2, 4, 8, and 16

Answer 12

good - so the largest number that divides into both is 16

Answer 13

yea

Answer 14

so we can take out 16 to get:\[0=16(3t-t^2)\]

Answer 15

now what goes into both t and \(t^2\)?

Answer 16

t?

Answer 17

correct again!
so we can take out a t to get:\[0=16t(3-t)\]

Answer 18

next, whenever something times something else equals zero, then you know that one of them must be equal to zero - agreed?

Answer 19

yea

Answer 20

so we have:\[0=16t(3-t)=16t\times(3-t)\]therefore we can say that either:\[16t=0\]or:\[3-t=0\]

Answer 21

alright

Answer 22

we therefore have two solutions for t - can you work them out?

Answer 23

so t = 3 and t = 0?

Answer 24

well done!
so we know the ball was on the ground when t=0 (i.e. at the start) and when t=3 (i.e. 3s after he kicked it in the air

Answer 25

does it make sense?

Answer 26

yep

Answer 27

ok - good

Answer 28

wait 1 more thing

Answer 29

yeah?

Answer 30

the answer is one of those fill ins so what should i write? t = 3?

Answer 31

in the question it says:

After how many seconds does the ball hit the ground?

so the answer must be t=3

Answer 32

t=0 is just the starting point

Answer 33

alright thanks

Answer 34

yw