Masses m and 2m approach each other at the same speed v and collide head-on. Find the final speed of mass 2m, if mass rebounds at speed 2v. g

The rebound speed of the mass 2m is v/2

Explanation:

I will designate the two masses as body A and body B.

mass of body A = m

mass of body B = 2m

velocity of body A = v

velocity of body B = -v    since they both move in opposite direction

final speed of mass A = 2v

final speed of body B = ?

The equation of conservation of momentum for this system is

mv - 2mv = -2mv + x

where x is the final momentum of the mass B

x = mv - 2mv + 2mv

x = mv

to get the speed, we divide the momentum by the mass of mass B

x/2m = v = mv/2m

speed of mass B = v/2

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