A bullet of mass m moving at 20 m/s embeds in a stationary block of mass 9m. The combined body subsequently rises vertically. Take g = 10 m/s². If the maximum rise is N/10 m, find N.

Question

G1 Physics · Accepted Answer

Stage 1: Perfectly inelastic collision. Momentum is conserved during the short collision: m(20) = (m+9m)V ⇒ 20m = 10mV ⇒ V = 2 m/s. Stage 2: Rise after collision. After the collision, mechanical energy is conserved during the upward motion: (1/2)(10m)V² = (10m)gh. Therefore h = V²/(2g) = 2²/(2×10) = 4/20 = 0.2 m = 2/10 m. Hence N = 2.