# Two fixed frictionless inclined planes making angle $30 ^{\circ}$ and $60 ^{\circ}$ with the vertical are shown. Two blocks A and B are placed on the two planes. What is the relative vertical acceleration of A with respect to B

$\begin{array}{1 1} a) 4.9 m/s^2 \text{ in horizontal direction} \\ b) 9.8 m/s^2 \text{in vertical direction} \\ c)zero \\d) 4.9 m/s^2 \text{in vertical direction }\end{array}$

a-acceleration along the inclined plane=$g \sin \theta$
Vertical component of acceleration is $g \sin ^2 \theta$
Therefore relative vertical acceleration of A with respect to B is
$g[\sin ^2 60 -\sin ^2 30]=\large\frac{g}{2}$$=4.9 m/s^2$
in the vertical direction
Hence d is the correct answer
edited May 23, 2014