Two fixed frictionless inclined plane making angles `30^(@)` and `60^(@)` with the vertical are shown in the figure. Two blocks A and B are placed on the two planes What is the relative vertical acceleration of A with respect to B ?

Explanation

`mg sin theta = ma rArr a = g sin theta`
where a is along the inclined plane
`:.` vertical component of acceleration is `g sin^(2) theta`
`a_(r) =a_(AB) =a_(A) -a_(B)`
`:.` relative vertical acceleration of `A` with respect
to `B` is `g (sin^(2) 60^(0) - sin^(2) 30^(0)) = (g)/(2) =4.9ms^(-2)`
(in vertical direction) .