A body of mass minitially at reststarts sliding from top of a smooth wedge of mass M,Height h and base angle θ .The wedge moves horizontally with const.acceleration a opposite to the direction of sliding.Calculate the time required for massm to reach the bottom and the total change of potential energy of mass m.

Obviously change in potential energy of body =work done by gravity on the system (wedge & body combined)= mgh.{as change in pot. energy of wedge is zero;it's still on the ground !!! }

For time calculation net force(& so net acceleration) on body down the incline is calculated first by changing the non-inertial(accelerated) frame into inertial one by introducing pseudo force  ma to the opposite of direction of acceleration of wedge taking body as a system with wedge as its frame in the FBD diagram.

As the direction of hor. accⁿ is not fully clear here,i'm giving answer for both possible case.

Consider wedge having its inclined plane being left as you draw it on screen here.(hypotenus on left & height on right)

CASE 1: accⁿ  a  applied to right in hor. direction.ma will be to left in hor. direction.

                  Taking x-axis along the plane  & y-axis perpendicular to it .

                  mgsinθ+macosθ=ma_net (force eqⁿin the x-direction)

or,             t=[(2h/sinθ)/(gsinθ+acosθ)]^1/2 using S=ut+1/2at² where S=h/sinθ ,a=a_net , u=0(starts from rest) with condition being gcosθ>asinθ

               as in the y-direction force eqⁿ  will give mgcosθ=masinθ+N

                  normal force=0 means body is no longer in contact of wedge,that's why the above condition .

 CASE 2: accⁿ  a  applied to left in hor. direction.ma will be to right in hor. direction.

                  mgsinθ-macosθ=ma_net (force eqⁿin the x-direction)

or,             t=[(2h/sinθ)/(gsinθ-acosθ)]^1/2 using S=ut+1/2at² where S=h/sinθ ,a=a_net , u=0(starts from rest) with no condition.

                   as in the y-direction force eqⁿ  will give mgcosθ+masinθ=N

                  normal force can never be zero unless a is (-ve) here which imply the first case.