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In the arrangement shown in fig., at a particular instant, the roller is coming down with a speed of 12ms^(-1) and C is moving up with 4ms^(-1) . At the same instant, it is also known that w.r.t. pulley P, block A is moving down with speed 3ms^(-1) . Determine the motion of block B (velocity ) w.r.t. ground.

A man rowed against a stream flowing 1 (1)/(2) km/hr to a certain point and then turned back, stopping 2 km, short of the place where he originally started. If the whole time occupied in rowing be 2 hr 10 min and his uniform speed in still water be 4(1)/(2) km/hr. Find the distance the man went up the stream.

A uniform bar of length 12 L and mass 48 m is supported horizontally on two smooth tables as shown in the figure. A small moth (an insect) of mass 8m is sitting on end A of the rod and a spider (an insect) of mass 16 m is sitting on the other end B . Both the insects start moving towards each other along the rod with moth moving at speed 2v and the spider at half of this speed. They meet at a point P on the rod and the spider eats the moth. After this the spider moves with a velocity v//2 relative to the rod towards the end A . The spider takes negligible time in eating the insect. Also, let v = L//T , where T is a constant having value 4 sec . The speed of the bar after the spider eats up the moth and moves towards A is