Question

A ball of mass m makes a head on elastic collision with a second ball at rest.  The first ball rebounds with a speed 0.450 times its original speed (in the opposite direction).  What is the mass of the second ball?

Please show algebra first :)

Answer 1

Refer the diagram :

Let mass of second ball is M and velocity is v.

Initial second body is at rest.

Applying conservation of linear momentum of system :

Final momentum of system = initial momentum if system

-------(i)

Also, the coefficient of restitution is e = 1.

-------(ii)

using the value of v from (ii) in (i) :

Therefore, the mass of second mass is 2.64 times the mass of first obejct. [answer]