As illustrated in the figure, the track is frictionless. Block B of mass 2m is situated at rest, while block A of mass m is propelled along the track with some initial speed. The collision between A and B is perfectly elastic. What initial velocity should be imparted to block A to awaken the sleeping man?

Step-by-step solution

Let v₀ be the initial velocity of block A. By conservation of mechanical energy, the velocity v₁ of block A just before colliding with block B is given by: 1 2 mv₀^2 + mgh = 1 2 mv₁^2 v₁^2 = v₀^2 + 2gh During the perfectly elastic collision between block A (mass m ) and block B (mass 2m , initially at rest), the velocity v_B of block B just after the collision is: v_B = 2m m + 2m v₁ = 2 3 v₁ For block B to reach the sleeping man at height h , its kinetic energy just after the collision must be greater than its pote