I was trying to solve a Mechanics question on Momentum.
Here is the question :
Two small smooth spheres A and B have equal radii and have masses m and km respectively. They are moving in a straight line in the same direction on a smooth horizontal table. The speed of A is $u$ and the speed of B is $\frac{2u}{3}$. Sphere A collides directly with sphere B. The coefficient of restitution between the spheres is $\frac{4}{5}$.
(i) Find the speed of A after the collision in terms of $u$ and $k$.
My Attempt
So I formed two equations, first the conservation of momentum:
$$mv_A+kmv_B=mu+\frac{2}{3}kmu$$
And coefficient of restitution formula :
$$v_A-v_B=\frac{4}{5}\left(u-\frac{2u}{3}\right)\tag{2}$$
Now I don't get the correct answer and the problem is that (2) is wrong according to answer book. The answer book states:
$$v_A-v_B=\frac{-4}{5}\left(u-\frac{2u}{3}\right)$$
You can see its quite similar to my equation, except that there is a - sign in front of the coefficient of restitution. Why is it negative?