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An elevator moves upward with an upward acceleration of 1ms2. At an instant when the velocity is 2ms1, a ball is thrown with initial velocity of 2ms1 with respect to the elevator at an elevation of 30. If the elevator is moving with a downward acceleration of g how will the motion be altered?
Option A: straight line w.r.t to elevator and projectile w.r.t ground.
Option B: projectile with respect to elevator and straight w.r.t ground.
Option C: projectile w.r.t both.
Option D: straight w.r.t both.

Answer
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Hint:The concept of relative motion is going to be used in this problem. The velocity of a body with respect to another moving body differs from its true velocity by a factor of the other body’s velocity.

Complete solution:
Here the case is very simple: the elevator is moving downwards with a velocity of 2ms1 and it has a downward acceleration of g so the elevator is undergoing a free fall motion.
Now when the ball is thrown from the elevator; the velocity of the elevator is 2ms1 downwards.
Now let us talk about the ball,
The ball is thrown in the upward direction at an angle of 30 from the elevator surface.
Also the velocity at that point of the ball is 2ms1 with respect to the elevator.
But the acceleration of the ball is ‘g’ downwards so the relative acceleration of both the bodies is zero.
Thus both bodies undergo a free fall motion with zero relative acceleration.
Thus the trajectory of the ball will be a straight line with respect to the elevator.
However, for someone on the ground frame i.e. outside the elevator the ball will look like it is undergoing a projectile motion.

Therefore option A is correct.

Note:
-If the relative acceleration was not zero then the motion would have been a projectile in both the cases.
-For a better understanding you must try and draw a diagram for the given case.
-In this case both the bodies appear to have been undergoing free fall with zero acceleration with respect to each other, so the relative motion was like a straight line.