Flag orientation for a boat observer Vs a ground observer

[vcsharp2003]

Homework Statement

The problem is as in screenshot below.

Relevant Equations

${\vec {V}}_{AB} = \vec V_A -\vec V_B$, where $\vec V_{AB}$ is velocity of A relative to B, and $\vec V_{A}$, $\vec V_{B}$ are velocities of A, B relative to ground

I am confused by the question. So, the first thing I am trying to understand is whether the flag direction will be same to a boat observer as to a ground observer.

I know that the flag will orient itself in the direction the wind is blowing towards, so the flag should always point in NE direction, no matter how the boat moves. But, that's not the answer. Or maybe, the ground observer will see the flag oriented in NE direction, but the boat observer will see it in a different orientation. Also, the problem doesn't mention whether the flag orientation to be found is relative to boat observer or ground observer.

Any hint on how to proceed would be much appreciated.

 

[kuruman]

I know that the flag will orient itself in the direction the wind is blowing towards, so the flag should always point in NE direction, no matter how the boat moves.

The flag will orient in the direction of the relative wind. If you are in a car moving to the North and you stick a small flag out an open window on a windless day, you will see the flag flutter as if a wind were blowing from the North.

 

[vcsharp2003]

The flag will orient in the direction of the relative wind. If you are in a car moving to the North and you stick a small flag out an open window on a windless day, you will see the flag flutter as if a wind were blowing from the North.

I see. If it was not windless, then how would the flag appear? I am guessing the flag direction will be in direction of the relative velocity of wind relative to boat ( i.e. flag direction as it appears to a boat observer).

 

[Lnewqban]

...
I am confused by the question. So, the first thing I am trying to understand is whether the flag direction will be same to a boat observer as to a ground observer.

Why are you trying to understand that?
I see no mention about those observers in the problem text.

 

[kuruman]

I see. If it was not windless, then how would the flag appear? I am guessing the flag direction will be in direction of the relative velocity of wind relative to boat ( i.e. flag direction as it appears to a boat observer).

Let's backtrack.
Say the boat is moving directly to the North and there is no wind. The flag will flutter so that a vector with its tail at the mast and its tip at the free edge of the flag will point South. The motion of the boat creates an artificial wind that points in the opposite direction of the boat's motion.

If there is a real wind blowing, the flag will flutter in the direction of the vector sum of the artificial and the real wind. It has nothing to do with whether the observer is on the boat or on shore. The orientation of the flag relative to the hull of the boat will be the same for both observers. However, the observer on the shore will feel only the real wind while the observer on the boat will feel the vector sum of the real and the artificial wind.

 

[vcsharp2003]

Why are you trying to understand that?
I see no mention about those observers in the problem text.

All motion is relative, so shouldn't observer be of consequence here?

 

[Lnewqban]

In this case, the flag is simultaneously under the influence of two air streams, each having a different orientation and velocity respect to each other and the ground.

 

[vcsharp2003]

Let's backtrack.
Say the boat is moving directly to the North and there is no wind. The flag will flutter so that a vector with its tail at the mast and its tip at the free edge of the flag will point South. The motion of the boat creates an artificial wind that points in the opposite direction of the boat's motion.

If there is a real wind blowing, the flag will flutter in the direction of the vector sum of the artificial and the real wind. It has nothing to do whether the observer is on the boat or on shore. The orientation of the flag relative to the hull of the boat will be the same for both observers. However, the observer on the shore will feel only the real wind while the observer on the boat will feel the vector sum of the real and the artificial wind.

That's very well explained. But, I need to read it multiple times to get it absolutely clearly. I really liked the concept of artificial wind and I think it should be in opposite direction to velocity of boat.

I think its similar to the scenario below. When rain falls vertically, the walking person will need to point the umbrella in direction of velocity of rain as it appears to the him/her. On the the other hand, a person standing on the ground would point the umbrella vertically. But the standing observer will see the walking person's umbrella inclined to the vertical, as will the walking person.

 

[kuruman]

I think its similar to the scenario below. When rain falls vertically, the walking person will need to point the umbrella in direction of velocity of rain as it appears to the him/her. On the the other hand, a person standing on the ground would point the umbrella vertically. But the standing observer will see the walking person's umbrella inclined to the vertical, as will the walking person.

Yes, it's a similar idea with the raindrops. Now think how a standing observer should hold the umbrella when there is a wind blowing parallel to the ground from the North.

 

[vcsharp2003]

Yes, it's a similar idea with the raindrops. Now think how a standing observer should hold the umbrella when there is a wind blowing parallel to the ground from the North.

Umbrella should point in a north direction if wind is blowing from north and of course, parallel to the ground

 

[vcsharp2003]

If there is a real wind blowing, the flag will flutter in the direction of the vector sum of the artificial and the real wind.

So, does this mean that the direction of velocity of wind relative to boat will decide the direction in which the flag will flutter? It seems like that.

 

[kuruman]

Umbrella should point in a north direction if wind is blowing from north and of course, parallel to the ground

Not necessarily. Don't forget that rain coming down also has a vertical component of velocity. A stationary person in rain with wind is the same situation as a running person in rain without wind. In the former case the wind is real whilst in the latter case the wind is artificial. Nevertheless, the way the umbrella is to be held is the same.

 

[kuruman]

So, does this mean that the direction of velocity of wind relative to boat will decide the direction in which the flag will flutter? It seems like that.

Yes, that's what it means.

 

[vcsharp2003]

Not necessarily. Don't forget that rain coming down also has a vertical component of velocity. A stationary person in rain with wind is the same situation as a running person in rain without wind. In the former case the wind is real whilst in the latter case the wind is artificial. Nevertheless, the way the umbrella is to be held is the same.

Oh ok, I get it. The rain velocity will be the vector sum of the wind velocity and the vertical rain velocity in windless air, which will then decide the direction of pointing of the umbrella.

 

[kuruman]

Oh ok, I get it. The rain velocity will be the vector sum of the wind velocity and the vertical rain velocity in windless air, which will then decide the direction of pointing of the umbrella.

Yes.