Hi, noob here!
I'm reasonably happy on 6e having seen the same answer here. I think the method is to use s=0m, not v=0, because the string becomes taut again when Q gets back to the same height it was at when P hit the ground. Then a=-g and u=4.2
I ended up not needing to factorise or use the quadratic formula afterwards too, since t=0 is clearly the solution you don't want. So divide through by t and you get 4.2 = 4.9t. Well, I really hope that's what you get, anyway.
Did I misread it, or didn't the last part of 4 ask for DEceleration so you get +1.75? Anyone else remember either way?