Two equal particles collide in mid-air. Immediately before collision their velocities are (6, 8) m/s and (−2, 4) m/s. They stick together. If their common speed just after collision is 2√N m/s, find N.
Physics · Center of maas , Momentum and Collision · collision and types of collision
JEE Mains NEET JEE Advanced

Question

Two equal particles collide in mid-air. Immediately before collision their velocities are (6, 8) m/s and (−2, 4) m/s. They stick together. If their common speed just after collision is 2√N m/s, find N.

Physics · Center of maas , Momentum and Collision · collision and types of collision

G1 Physics · Accepted Answer

Because the particles stick together, the collision is perfectly inelastic. During the short collision interval, external impulse is negligible, so momentum is conserved. For equal masses m and m: 2mV = m(6,8) + m(−2,4). Therefore V = [(6,8)+(−2,4)]/2 = (4,12)/2 = (2,6) m/s. Common speed: |V| = √(2²+6²) = √40 = 2√10 m/s. Hence N = 10.