A point mass of 1 kg moving horizontally with speed u hits a pendulum bob of mass 2 kg initially at rest. The collision is perfectly elastic. After the collision, the pendulum bob swings upwards and reaches a maximum vertical height of 0.8 m. Taking g = 10 ms ⁻² , the initial speed u of the 1 kg mass is:

Step-by-step solution

First, find the velocity of the 2 kg bob just after the collision using conservation of mechanical energy during its upward swing: 1 2 M v_M^2 = M g h v_M = 2gh = 2 10 0.8 = 16 = 4 ms ⁻¹ . For a 1D elastic collision, the velocity of a target mass M initially at rest, struck by a mass m moving with initial velocity u , is given by: v_M = 2m m + M u Substituting the given values ( m = 1 kg, M = 2 kg, v_M = 4 ms ⁻¹ ): 4 = 2 1 1 + 2 u 4 = 2 3 u u = 6 ms ⁻¹ . Answer: 6 ms ⁻¹