A 5.25-kg ball, moving to the right at a velocity of +2.10 m/s on a frictionless table, collides head-on with a stationary 7.60-kg ball. Find the final velocities of the balls if the collision meet the following conditions.

(a) elastic
5.25-kg ball = Incorrect: Your answer is incorrect. m/s
7.6-kg ball = m/s

(b) completely inelastic

1 answer

momentum
5.25*2.1+O=(5.25)V1+7.60(V2)
energy:
1/2 5.25*2.1+0=1/2 5.25v1^2 + 1/2 7.6v2^2
or 5.25*2.1+0= 5.25v1^2 + 7.6v2^2
In the first equation:

v2=(5.25(2.1-V1)/7.6

so now, square that
v2^2=.69^2(2.1^2-4.2v1+vi^2)
and put it into
5.25*2.1+0=1/2 5.25v1^2 + 7.6v2^2
or
5.25*2.1+0=1/2 5.25v1^2 + 7.6.69^2(2.1^2-4.2v1+vi^2)
Now, do the algebra and get it to a quadratic form and find the two solutions for v1.
Then go back and find V2