Need help - forces question?

Question

A ball of mass 5.0 kg with a velocity of 8.0 m/s [E] collides head on with another moving ball with mass 4.0 kg. The collision lasts 0.1 s and the 5.0 kg ball rebounded with a velocity of 5.0 m/s [W]. The 4.0 kg ball rebounded with a velocity of 4.0 m/s [E]. Calculate the velocity of the 4.0 kg ball before the collision.

Please help; I'd really appreciate it. I got some random answer of 12.25 m/s when I tried to do it but honestly, I... don't know what I'm doing.

Thanks! :)

Answer 1

You got the right answer as long as you also qualify that it is a vector quantity, so it has direction. In this case, you have it as positive, so it is in the direction that the 4.0 kg ball was moving before the collision.

The derivation is using conservation of momentum. Always take care with the signs.
Your sign convention is as stated above.

Momentum before equals momentum after

m1*v1i+m2*v2i=m1*v1o+m2*v2o
v1i= -8.0
v1o = 5.0
v2o = -4

plugging in
5*(-8)+4*v1i=5*5+4*(-4)
-40+4*v1i=25-16
v1i=(25-16+40)/4
=12.25

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