Two identical carts are moving on parallel smooth tracks with velocities `u_(1) = 10 ms^(-1) and u_(2) = 15 ms^(-1)`. The empty carts (with drivers) have mass `3m` each. Each cart has a sack of mass m kept at end A and end D (see figure). At the instant the carts being to cross, the sack in cart 1 is the thrown perpendicular (relative to cart 1) with some unknown velocity and it lands on cart 2 at its end D after a time `t_(0)`. Immediately after the sack lands into cart 2, the original sack in cart 2 is thrown perpendicularly (relative to cart 2) towards cart 1 in identical fashion. The sack lands on cart 1 at point M, a time `t_(0)` after the throw. Assume that the carts are constrained to move in straight lines.
(i) Find length BM if length of each cart is L
(ii) Find the velocity of cart 1 after the sack thrown from cart 2 lands on it.

Answer

(i) `(L)/(5)`
(ii) `5 m//s^(-1)`