Since, collision is head on, then particle
A will continue moving along the same line as before the collision, but there will be a change in the magnitude of its velocity vector. Let particle
A starts moving with velocity
v1 and particle
B with velocity
v2 after collision, then from conservation of linear momentum,
mu=mv1+mv2 or
u=v1+v2.....(i)
From the given condition,
i.e
η= ⇒η=1− ⇒v12+v22=(1−η)u2.....(ii)
Now solving Eqs. (i) and (ii), we get
v1=5m∕ s