A particle of mass 4 M which is initially at rest explodes into three pieces of masses M , M and 2 M . The equal masses move along X - and Y - axes with velocities 4 m s - 1 and 6 m s - 1 respectively. The magnitude of the velocity of the heavier mass is

Step-by-step solution

Recall the condition of conservation of linear momentum in x - axis is, 0 = M × 4 + 0 + 2 M × u cos θ u cos θ = 2 . . . 1 and a vertical component, 0 = 0 + 6 M + 2 M u sin θ u sin θ = 3 . . . 2 from equation 1   &   2 ⇒ u 2 cos 2 θ = 4   &   u 2 sin 2 θ = 9 ⇒ u 2 cos 2 θ + u 2 sin 2 θ = 13 ⇒ u 2 = 13 ⇒ u = 13   m   s - 1