$a_{A,B}=a_{A,E}+a_{E,B}$ - Relative acceleration

Question

When two balls $A,B$ are moving under gravity , Find acceleration of $A$ relative to $B$ (That is $a_{A,B}$)

a) Both $A$ and $B$ are moving down !

b) $A$ moves upwards and $B$ moves downwards (above $A$)

For $a)$ $a_{A,B}=a_{A,E}+a_{E,B}$

$a_{A,B}=g+(−g)=0$ That is there is no relative acceleration between $A$ and $B$.

But for $b)$ is it $2g$ or zero ?

Answer 1

I have never heard of the physical concept "acceleration of A relative to B". This is because in Newtonian mechanics acceleration is absolute. Your two balls experiment the same acceleration, irrespective of whether they are going up or down. So the relative acceleration must be zero.