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.

Acceleration-
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,
y3=x2,


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.