- #1
cr7einstein
- 87
- 2
Hi all!
I was having a conversation with a (rather young) friend about the following imaginary situation- suppose you are in a helicopter, at rest relative to the ground. So you are basically seeing a 'top' view. Say you have a a wall fixed to the ground, and it is kept in the middle of a moving river, parallel to the flow which has a horizontal speed ##v_m##(relative to the ground). Suppose it is moving rightward. Note that the wall doesn't move relative to you. Now, there is a boat which is moving through the river, such that it's velocity relative to the river is purely vertical (i.e. its speed relative to the ground is is ##(v_y)^2+(v_m)^2##), and so relative to the helicopter, it follows a 'diagonal' path, moving towards the wall. The property of the wall is such that if there was no water ( and the boat could somehow still move), the boat would rebound exactly at the same speed, making the same angle with the wall as before (so something like an elastic collision).
Now, what happens in the presence of the river? For you inside the helicopter, does it still rebound at the same angle with which it hits the wall?
My argument is yes, it does. Because, if you were 'in the water', you would see the ball go straight up to the moving mirror and come back down the same way, so no change in angle. Since the helicopter is also an inertial frame, and all of them are equivalent, there should still be no change in angle after collision.
His argument is that after the collision, the boat STARTS moving out with the same speed as before, but this new velocity is immediately affected by the river velocity, and so it rebounds at a different angle (i.e. makes a greater angle with the normal through the wall; it has been 'carried' further to the right.)
Now, I do not want to use conservation of momentum to back up my argument. Is there a simple physical argument I could use to point out the mistake in his reasoning? I tried to show him the component of the velocity in direction of flow remains unchanged, and the component directed towards the wall gets 'reversed'. But he still thinks that the 'reversed' component will be further deviated to the right by the river. I tried explaining that the horizontal component is doing just that, but perhaps there is a better, more precise argument to explain this. Any help would be appreciated.
Thanks in advance!
I was having a conversation with a (rather young) friend about the following imaginary situation- suppose you are in a helicopter, at rest relative to the ground. So you are basically seeing a 'top' view. Say you have a a wall fixed to the ground, and it is kept in the middle of a moving river, parallel to the flow which has a horizontal speed ##v_m##(relative to the ground). Suppose it is moving rightward. Note that the wall doesn't move relative to you. Now, there is a boat which is moving through the river, such that it's velocity relative to the river is purely vertical (i.e. its speed relative to the ground is is ##(v_y)^2+(v_m)^2##), and so relative to the helicopter, it follows a 'diagonal' path, moving towards the wall. The property of the wall is such that if there was no water ( and the boat could somehow still move), the boat would rebound exactly at the same speed, making the same angle with the wall as before (so something like an elastic collision).
Now, what happens in the presence of the river? For you inside the helicopter, does it still rebound at the same angle with which it hits the wall?
My argument is yes, it does. Because, if you were 'in the water', you would see the ball go straight up to the moving mirror and come back down the same way, so no change in angle. Since the helicopter is also an inertial frame, and all of them are equivalent, there should still be no change in angle after collision.
His argument is that after the collision, the boat STARTS moving out with the same speed as before, but this new velocity is immediately affected by the river velocity, and so it rebounds at a different angle (i.e. makes a greater angle with the normal through the wall; it has been 'carried' further to the right.)
Now, I do not want to use conservation of momentum to back up my argument. Is there a simple physical argument I could use to point out the mistake in his reasoning? I tried to show him the component of the velocity in direction of flow remains unchanged, and the component directed towards the wall gets 'reversed'. But he still thinks that the 'reversed' component will be further deviated to the right by the river. I tried explaining that the horizontal component is doing just that, but perhaps there is a better, more precise argument to explain this. Any help would be appreciated.
Thanks in advance!
