At the highest point, a projectile of mass 4m has velocity (20, 0) m/s. It explodes into two fragments of masses m and 3m. Immediately after the explosion, the fragment of mass m moves vertically upward with velocity (0, 20) m/s. If the speed of the 3m fragment is 20√N/3 m/s, find N.
Physics · Center of maas , Momentum and Collision · momentum and conservation of momentum
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Question

At the highest point, a projectile of mass 4m has velocity (20, 0) m/s. It explodes into two fragments of masses m and 3m. Immediately after the explosion, the fragment of mass m moves vertically upward with velocity (0, 20) m/s. If the speed of the 3m fragment is 20√N/3 m/s, find N.

Physics · Center of maas , Momentum and Collision · momentum and conservation of momentum

G1 Physics · Accepted Answer

The external impulse during the explosion is negligible, so vector momentum is conserved. Initial momentum is p(initial) = 4m(20, 0) = (80m, 0). Momentum of the m-fragment is p₁ = m(0, 20) = (0, 20m). Hence momentum of the 3m-fragment is p₂ = (80m, 0) − (0, 20m) = (80m, −20m). Therefore its velocity is v₂ = p₂/(3m) = (80/3, −20/3) m/s. Its speed is √[(80/3)² + (20/3)²] = (20/3)√(16+1) = 20√17/3 m/s. Hence N = 17.