Figure shows a block A constrained to slide along the inclined plane of the wedge B shown. Block A is attached with a string which passes through three ideal pulleys and connected to the wedge B. If wedge is pulled toward right with an acceleration a, find
(a) the acceleration of the block with respect to wedge
(b) the acceleration of the block with respect to ground.

Explanation

(a) Length of (1) and (3) will increase at the cost of part 4. Hence decreases in length of (4) will be twice of increase in lengths of either 1 or 3.
So, `a_(A)=2a`.

(b) Accleration of block w.r.t ground
`a_(1) = sqrt(a^(2)+a_(A)^(2)+2a_(A) cos (190-theta))= asqrt(5-4 cos theta)`.