Question

this question is kinda...queer

Esmeralda dropped a ping pong ball from a height of 4 feet. She tracked the height of the ball and the elapsed time. The ball hit the floor at 2 seconds and then bounced. At 4 seconds, the height was 4 feet.

Write a piecewise function to describe the path of the ping pong ball.

please explain. thank you.

Answer 1

which part are you having trouble with?

Answer 2

writing the piecewise function.
and why the ping pong ball would bounce from 4 feet to 4 feet again after 4 seconds

Answer 3

they are assuming that the ping pong ball bounces without loss of energy. While this is unlikely, this is the assumption

Answer 4

do you know the equation for the path of a falling object?

Answer 5

no.

Answer 6

eh. this is not really how hte ball would fall, but let's just assume a linear fall speed.

Answer 7

does the graph make sense?

Answer 8

not really..so the ball bounces the same height, each at 4 seconds?

Answer 9

yes. this is a height versus time graph

Answer 10

okay. how am i supposed to solve it

Answer 11

break it up into piecewise functions.

Answer 12

so the first equation is y=-2x+4
the second equation is y=2x-4

Answer 13

what is a piecewise function i don't really know

Answer 14

a piecewise function is a function that's basically based on pieces.

Answer 15

in this case you are only interested in the path of the ball from t=0 to t=4.
simply put, you break up the function into two parts

Answer 16

it can be more than 2, but we only have 2 lines we need to work with, so we'll use 2.

Answer 17

what is x and what is y in your equation?
also, how MANY pieces?

Answer 18

however many pieces you want. you usally try to limit the amount of pieces to what you need.
x in the equation is time. y in the equation is height

Answer 19

also, is the "4" in your equation the 4 feet? or the 4 seconds?

Answer 20

the 4's are actually arbitrary numbers that are based upon the equations of the first two line segments

Answer 21

i'm lost

Answer 22

ugh. I'm too sleepy to give an in-depth explanation. @Compassionate help

Answer 23

is 4 the feet?

Answer 24

No. 4 is a number that you get when you model the lines. I'm not sure I can explain it better

Answer 25

are you the both equations about the height?

Answer 26

uhh.
y describes a height
tx describes a time.

Answer 27

oh.
sorry i kinda feel guilty..it's not like you are REQUIRED to help me. however, i AM almost done here...i'll give you a medal if you keep helping? sorry i really need to get this. i'm almost done asking qus.

Answer 28

ok. I will give you the piecewise definition I have formed. I usually don't resort to giving answers, but I am running out of time

Answer 29

thanks SO muh

Answer 30

so the first equation is y=-2x+4
the second equation is y=2x-4