Verified answer

for elastic collisions, coefficient of restitution is 1

let u be initial velocity and v be final velocity (after collision)

by conservation of momentum, we have -->

m1u1 + m2u2 = m1v1 + m2v2

and by conservation of energy, we have -->

1/2{m1(u1)^2} + 1/2{m2(u2)^2} = 1/2 {m1(v1)^2} + 1/2{m2(v2)^2}

solving above equations, we get -->

v1 = { u1 (m1 - m2) + 2m2u2 } / { m1+m2 }

v2 = { u2 (m2 - m1) + 2m1u1} / { m1+m2 }

(consider the signs and direction too)

put the values and youll see that v1 = 2 m/s and v2 = 2 m/s but both in opposite direction to each other and also opposite to their initial velocities...

EDIT -->

Sorry.. i put the values wrong last time..

put m1 = 7m , m2 = m, u1 = 2 and u2 = -2 ... solving now, we get -->

v1 = 1 m/s and v2 = 5 m/s both in same direction and in the direction of u1 (ie direction of red ball initially)

BY the law of momentum conservation:-

=>m(r)u(r) + m(b)v(b) = m(r)v(r) + m(b)v(b)

=>7m x 2 + m x (-2) = 7m x v(r) + mv(b)

=>7v(r) + v(b) = 5 --------------(i)

for elastic collision:-

=>v(r) - v(b) = u(r) - u(b)

=>v(r) - v(b) = 2-(-2)

=>v(r) -v(b) = 4 ----------------(ii)

=>By (i) + (ii) :-

=>8v(r) = 9

=>v(r) = 9/8 = 1.125 m/s (in the direction of initial velocity)

By (ii) :-

=>v(b) = -2.875 m/s (in the direction of initial velocity)