# Physics

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A 0.0600 kg tennis ball, moving with a speed of 2.50 m/s, has a head-on collision with a 0.0900 kg ball initially moving away from it at a speed of 1.00 m/s. Assuming a perfectly elastic collision, what is the speed and direction of each ball after the collision?

-I was given that the answer for the speeds of the balls are .70m/s and 2.2m/s.

equations:

m1v1+m2v2 = m1v1'+m2v2'
V1-V2=V2' - V1'

My attempt:

with the given, I know that
m1= .06 kg
m2=.09 kg
v1= 2.5 m/s
v2= 1.0 m/s
after this, I got to .135=m1v1'+m2v2'
and 1.5= V2'-V1'

• Physics -

I agree with this
m1v1+m2v2 = m1v1'+m2v2'
I disagree with this:
V1-V2=V2'-V1'

where in the world did that come from?

• Physics -

I asked someone else for help on this problem and they told me to use that equation. That's even what they wrote down for me. I agree it doesn't make sense.

Anyways the initial and final mass will stay the same right? So I will be at...

135=(.06)v1'+(.09)v2'

• Physics -

Now you have one other equation you can use, the magic equation conservation of energy is true

Intial KE= final KE
You know initial KE. Final ke, 1/2 m1*V1'^2 + 1/2 m2 v2'^2 is equal to that initial.
solve for v2' in terms of all the other stuff, then put that v2' into the conservationof energy equation (yes square v2') It is messy algebra, you will get a quadratic you can solve (quadratic equation).

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