We have 3m V = mv1 + mv2 + mv3 , where the velocities are in vector form.
Let one particle continue moving in the same direction as the 3m mass and let the other two travel at angles q2 and q3 respectively with the original direction.
Therefore 3v = v1 + v2 cos q2 + v3 cos q3 ---(1)
In the perpendicular direction we have
v2 sin q2 = v3 sin q3 ----(4)
Also 3 m v2 (3/2) = m (v21 + v22 + v23) ?(5)
From 1 for V1 to be maximum q2 and q3 should be p each and therefore we get
3v = v1 - v2 - v3 from 1.
Eliminating v3 from the above equations we get
9v2 / 2 = v12 + v22 + (3v - v1 - v2)2
make this a quadratic equation in v2 and apply the condition for real roots we get the value of v1 (maximum).
Moderation Team
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