Solving Motion of Block A on Wedge B

[hav0c]

Homework Statement

A block A of mass m is placed over a wedge B of same mass m. Assuming all surface to be smooth. The displacement of block A is 1 sec if the system is released from rest is :

Homework Equations

The Attempt at a Solution

i have made fbds and have the relations-
1. ma₁=(g-N₁)/m
2.N₁cos θ+mg cosθ=N₂
3.ma₂=sinθ(mg+N₁)
now I am stuck

 

[consciousness]

There is one more equation. The blocks stay in contact so their velocities perpendicular to the contact are same. What can you say about the relative acceleration perpendicular to the contact?

 

[hav0c]

There is one more equation. The blocks stay in contact so their velocities perpendicular to the contact are same. What can you say about the relative acceleration perpendicular to the contact?

What velocities are the same?
I don't get it
EDIT:Thanks i got it A1=a2sintheta

 

[Saitama]

Homework Statement

A block A of mass m is placed over a wedge B of same mass m. Assuming all surface to be smooth. The displacement of block A is 1 sec if the system is released from rest is :

Homework Equations

The Attempt at a Solution

i have made fbds and have the relations-
1. ma₁=(g-N₁)/m
2.N₁cos θ+mg cosθ=N₂
3.ma₂=sinθ(mg+N₁)
now I am stuck

Your first equation has a dimensional error.

I don't think the second equation would do any good. Your third equation is fine. Apply the constraint that blocks A and B stay together during the motion.