Question

With the minimum velocity should block be projected from left end A towards end B such that it reaches the other end B of conveyer belt moving with constant velocity v. The friction coefficient between block and belt is $\mu$.

Answer 1

Let initial velocity be 𝑢 , for the minimum initial projection speed (w.r.t belt), velocity of the body at the other end should be zero w.r.t the conveyor belt, which is moving with 𝑣 velocity in opposite direction. There will be slipping, hence the retardation will be -𝜇𝑔with the total length of 𝑑

⟹𝑢2=2𝜇𝑔𝑑

⟹𝑢=𝜇𝑔𝑑