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Q. A ball is dropped from an elevator moving upward with acceleration ' $a$ ' by a boy standing in it. The acceleration of ball with respect to [Take upward direction positive]

Motion in a Straight Line

Solution:

image
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.
$a_{\text {ball } G}=a_{\text {ball }}-a_{\text {ground }}=-g-0$
$a_{ bG }=-g$
$a_{b G}=$ 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.