i, j are unit vectors along x, y axes
let initial velocity of both charges be v i
Impulse = change in momentum
q1Et = m[(v/2)(cos60 i + sin60 j) - v i] ........(let its velcity nw makes a positive angle 60 with x-axis )
or Et/m = 1/q1[(-3v/4 i + rt(3)v/4 j].............................(1)
Let for q2, final velocity = v2 (vector)
so, Et/m = 1/q2 [ v2 - v i]..........................................(2)
1/q1[-3v/4 i + rt(3)v/4 j] = 1/q2[v2-v1]
v2 = (v - 3q2v/4q1) i + rt(3)q2v/4q1 j
Since, its direction has changed by 90deg, i component =0
v - 3q2v/4q1 = 0
q2/q1 = 4/3
So, v2 = rt(3)v/4 * (q2/q1) j = rt(3)v/4 * 4/3 = v/rt(3)
mag of vel changes by a factor of 1/rt(3)