Can someone explain the answers to question 12 and 13 of hc verma rest & motion objective 1?

For q13, make the triangle between one pulley, mass and the point straight above it.Differentiate length of string and you'll get the solution.

Try it.If you dont get it, visit :

http://www.goiit.com/posts/list/mechanics-please-fin-velocity-33091.htm

For q12, use :

 mod(V_ab) =rt(v_a² + v_b² - 2v_av_b cos @.)...............ie relative motion formula..

So for maximum magnitude velocity, @ =90..

Thus he should swim straight!

Simple isnt it,once you know the formula?