Upward direction \(\rightarrow\) Positive

Negative direction \(\rightarrow\) Negative

If a person is observing from ground then, for him the acceleration of ball is in the downward direction.

\(a_{ ball G}=a_{ ball }-a_{\text {ground }}=-g-0\)

\(a_{ bG }=-g\)

\(a_{b G}=\) Acceleration of ball w.r.t. ground.

\(a_{\text {ball boy }}=a_{\text {ball }}-a_{\text {boy }}=-g-a\)

\(a_{b b}=-(g+a), a_{b b}=\) Acceleration of ball w.r.t. boy.