2-body collision: Min and Max speed

[unscientific]

Homework Statement

A ball of mass M traveling at non-relativistic speed v elastically collides with a stationary ball of mass m.

(a)Show that the maximum speed which the second ball can have is:

2Mv/(M+m)(b)What is the minimum speed?

The Attempt at a Solution

(a)
Method 1

Go into ZMF frame:

step 1: find V_CM
step 2: u₂' = u₂ - V_CM
step 2: p_i = p_f = 0
step 3: v₂' = -u₂
step 4: go back into lab frame by adding V_CM

Method 2

1)Speed of approach = speed of separation
2)conservation of momentum
3)done.

But the puzzling thing is that why is this the maximum speed? Isn't this the actual acquired speed?

(b)
Do we assume a head-on collision? If it is a head-on collision won't the speed be the same as part (a)?

assuming a non head-on collision by including angles and stuff doesn't help..

 

[mfb]

If you assume a head-on collision where the second ball travels in the initial direction of ball 1, this is the maximal speed.
Every other collision will give a lower speed.

 

[unscientific]

If you assume a head-on collision where the second ball travels in the initial direction of ball 1, this is the maximal speed.
Every other collision will give a lower speed.

so for part (b) it isn't a head-on collision?

 

[mfb]

Right ;)