Mass on wedge on incline problem

[uhohitzluke]

Homework Statement

The problem is provided in the pdf attachment

Homework Equations

I know how to solve frictionless problems with a single mass on an incline but this is just too advanced for me. (especially with two inclines of different angles)

The Attempt at a Solution

I drew free body diagrams of A and B separately. I'm not sure how I'm supposed to find the summation of forces in the x and y directions when both inclines have different angles. I'm totally lost and I have to turn this in tomorrow ):

 

[danielakkerma]

Hi there, welcome to the forum.
Whenever there's a question concerning multiple masses, especially those featuring some stacked on one another & requiring simultaneous computation of acceleration/relative velocities, that sort of thing, it always helps to distinguish, whenever possible between convenient frames of reference; By that I mean:
Firstly, using the angle of the larger wedge(A in your case), find the total acceleration of the system, which has a cumulative mass of A+B(and you can assume, for the initial duration of the motion, that they'll safely travel together). This will generate, however, an inertial acceleration separately on the mass B, acting oppositely on it, which you would then incorporate to find out its acceleration solely(using its angle, B's). Relative velocity, as you recall is determined by:
$\large<br /> V_{b,a} = V_b-V_a$
And the query is readily resolved.
I hope that clears matters somewhat,
Daniel