How do I find the speed of a block at the bottom in a half circle cavity?

Jun 2017
300
6
Lima, Peru
You are right, we need the mass of the (blue) block.

@Chemist116: I just have to ask.. Where are you getting these problems from?
In response to your curiosity the original source doesn't really say where did it got it from (as it comes from a collection of problems) but apparently (after looking into that) it seems to come from a rare soviet era textbook from the 70s or mid 80s.

I did a search on bookfinder and I got this





@skeeter was particularly interested in finding the original source of this problems. I cannot guarantee that problems from my class and homework are in those books but judging that there is one which matched those there could be a big chance that it will also be more.

This almost begs for a simple Lagrangian methods problem. It is not obvious about how to do it otherwise.
When you mentioned a Lagrangian methods, did you mean this?

Why is it so?.

Is your instructor a sadist or something?
I guess... who knows the reason for such difficulty!. I do not like it.
 
Jun 2017
300
6
Lima, Peru
${\color{red}mgR} = \dfrac{1}{2}[mv^2 + MV^2]$

also, $\vec{p_0} = \vec{p_f} = 0$
Thanks for coming to the rescue!. mind checking again the problem of the person atop the platform in the ice rink?. How did you interpreted?. Because the more I look the wording (even though I did transcribed it word by word) seems very misleading. I appreciate if @DarnItJimImAnEngineer could also look into that.