1. The problem statement, all variables and given/known data A particle P is sliding down a frictionless hemispherical bowl. It passes the point A at t = 0. At this instant of time, the horizontal component of its velocity is v. A bead Q of the same mass as P is ejected from A at t=0 along the horizontal string AB, with the speed v. Friction between the bead and the string may be neglected.Which bead reaches point B earlier? 2. Relevant equations 3. The attempt at a solution Let θ be the angle which the particle P makes with the vertical . N-Mgcosθ = Mv2/R Mgsinθ = -Mvdv/dx or,Mgsinθ = -Mvdv/Rdθ RMgsinθdθ = -Mvdv ∫β0RMgsinθdθ = -∫uwMvdv , where β is the initial angle ; u is the initial velocity and w is the velocity at the bottommost point . But how to relate initial velocity 'u' with the initial horizontal component of velocity 'v' . I am not sure if this is the correct approach. I would be grateful if someone could help me with the problem.