A bolt drops from the ceiling of a moving train car that is accelerating northward at a rate of 2.50m/s^2. (a) What is the acceleration of the bolt in relation to the train car? (b) What is the acceleration of the bolt relative to the Earth? (c) Describe the trajectory of the bolt as seen by an observer fixed on the Earth.

Question

ujjwal · Answer

The acceleration of bolt in relation to train car should be 9.8 m/s^2 downwards...
The acceleration of bolt with respect to earth should also be 9.8 m/s^2.

The trajectory of bolt should be parabolic for a fixed observer on earth since the bolt will have certain initial forward velocity (it is dropped in a 'moving' train) and it will accelerating downwards at 9.8 m/s^2 at the same time..

Correct me if i am wrong @Vincent-Lyon.Fr

vincent-lyon.fr · Answer

Since the train is accelerating, the acceleration relative to the train-car will not be vertical downwards.

All other assumptions are correct.

ujjwal · Answer

Oh yes.. I just realized it.. Thanks @Vincent-Lyon.Fr !!

anonymous · Answer

Thanks!
But I'm still having a doubt about the acceleration of the bolt relative to the Earth.
Do I have to add the acceleration of the train (2.5 northwards) to the acceleration of gravity (9.8 downwards) ?
Or do I have to consider the acceleration of the train to the other side? (2.5 southwards)

ujjwal · Answer

The only force acting on bolt once it leaves the ceiling is 'gravity'.. So, it will be accelerated only under the action of gravity.. and it's acceleration relative to earth will be 9.8 m/s^2 downwards..
The train's acceleration has nothing to do with the bolt once the bolt leaves the ceiling!

anonymous · Answer

Sorry, I mean the acceleration of bolt in relation to train car.
How can I find it? Adding 9.8 down and 2.5 north?

ujjwal · Answer

*south

anonymous · Answer

Thanks! :D