Find the acceleration of block B as shown in fig. (a) and (b) relative to block A and relative to ground if block A is moving toward right with acceleration a.

Explanation

(i) Length of (5) will decrease at the cost of increases in length of (1) and (3).
Hence, acceleration of B w.r.t. A:
`a_(BA)=2a`
(ii) Acceleration of B w.r.t ground
`a_(BA)=a_(B)-a_(A) implies -2a=a_(B)-a`
`implies a_(B)=-a`

(i) Length of 4 will decrease at the cost of 1,2,and 3 hence
`a_(BA)=3a`

(ii) `a_(BG)= sqrt(a^(2)+a_(BA)^(2)+2aa_(BA) cos theta)=a sqrt(10+6 cos theta)`.