Question

A lift accelerating downwards with acceleration $a$. A man in the lift throws a ball upward with acceleration ${a_0}$ $({a_0} < a)$. Then acceleration of ball observed by observer, which is on earth, is
A. $(a + {a_0})$ upward
B. $(a - {a_0})$ upward
C. $(a + {a_0})$ downward
D. $(a - {a_0})$ downward

Answer 1

Hint: First find out the direction of the acceleration with respect to the observer. After doing this the resultant acceleration or the magnitude of the acceleration can be calculated just by adding/subtracting according to the conditions given in the problem (in this case it is subtracting).

Complete step by step answer:
In the question it is said that a lift accelerating downwards with acceleration $a$. A man in the lift throws a ball upward with acceleration ${a_0}$ $({a_0} < a)$. We need to find out what would be the acceleration of the ball observed by the observer located on earth.So, we see that the lift is accelerating in the downward direction. When a man is throwing the ball upwards, for him (inside the lift) the ball seems to be accelerating in an upward direction.

But for an observer who is outside the lift the ball seems to be moving downward along with the lift. So, from this part it is clear that the motion is in downward direction.Hence, we can say that option A and option B are incorrect for this particular question. Now we need to calculate what would be the magnitude of acceleration observed by the observer on earth.From the given question,
Acceleration of the lift $ \to a$
Acceleration of the ball $ \to {a_0}$
where, $({a_0} < a)$
So, the acceleration observed by observers on earth is given as: ${a_{obs}} = a - {a_0}$.
Therefore, the acceleration of the ball observed by an observer on earth is $(a - {a_0})$downwards.

So, option D is the correct answer.

Note: The solution would have been different if the question would have been asked with respect to some other observer. So, it is necessary to solve the sum with reference to the observer’s location or position.Acceleration is a vector quantity as it has both magnitude and direction. It is also the second derivative of position with respect to time or it is the first derivative of velocity with respect to time.