As shown in the figure, a small block of mass m is set in motion with a speed v along the horizontal portion of a bigger block of mass M that rests on a horizontal floor. The curved segment of the surface is semicircular. All surfaces are frictionless. Determine the speed of the bigger block at the instant the smaller block reaches point A on the surface.

Step-by-step solution

Since all surfaces are frictionless, there is no external force acting on the system (smaller block and bigger block) in the horizontal direction. Therefore, the horizontal component of the total linear momentum of the system is conserved. At point A, the tangent to the semicircular surface is vertical. This means that the velocity of the smaller block relative to the bigger block is purely vertical. Thus, at the instant the smaller block reaches point A, its horizontal velocity is exactly equal to the horizontal v