Two particles A and B are moving at a speed of 5 m/s along the paths shown in the figure.If B is accelerating at 8 m/s2 and A is decelerating at 6 m/s2, determine the relative acceleration of B with respect to A.

1) -1.5199i - 2.633j.
2) -2.5178i - 2.345j.
3) -1.3456i - 4.234j.
4) -7.4326i - 2.145j.

The x,y axes are located at an arbitrary fixed point.The translating frame of reference x',y' is attached to particle A.
For the given figure,

This is the angle made by the acceleration vector of A to the positive x direction.
The angular acceleration is given by the formula
an = v2/r,
r is the instantaneous radius of motion.

an = 25/6.944 = 3.6 m/s2.

aA = -ancos36.87i + ansin36.87j - atsin53.13i- atcos53.13j

The acceleration of B is
aB =aA + aB/A.
-8i = -3.6cos(36.87)i + 3.6sin(36.87)j - 6cos(53.13)i - 6sin(53.13)j + aB/A.
aB/A = -1.5199i - 2.633j
This is the relative acceleration vector of B with respect to A.