How Should a Ferryboat Navigate a River with Flowing Water?

[negation]

Homework Statement

A ferryboat sails between towns directly opposite each other on a river, moving at speed v_actual relative to the water.
a) Find an expression for the angle it should head at if the river flows at speed v_river.
b) What is the significance of your answer if v_river > v_actual?

The Attempt at a Solution

a) v_effective = v_actual + v_river
v_effective = hypotenuse, v_river = opposite, v_actual = adjacent
Θ = arctan ( v_river/v_effective)

b) How is it possible for the adjacent to be > than the hypotenuse?

 

[voko]

What must the direction of the effective velocity be? What is the direction of the flow? Draw if unsure.

 

[negation]

what must the direction of the effective velocity be? What is the direction of the flow? Draw if unsure.

 

[voko]

If the effective velocity is not at the right angle to the flow velocity, can the ferry serve towns directly opposite each other on a river?

 

[negation]

If the effective velocity is not at the right angle to the flow velocity, can the ferry serve towns directly opposite each other on a river?

It can't. v_effective is calculated on the premise of v_river being perpendicular to v_effective. If the position of the town is shifted, the angle between v_actual and v_effective will change and therefore the ratio between v_effective and v_river will change

 

[voko]

The goal of the ferry is to connect the towns. So its effective velocity must be directed "across the river", which means it must be perpendicular to the velocity of the flow.

 

[negation]

The goal of the ferry is to connect the towns. So its effective velocity must be directed "across the river", which means it must be perpendicular to the velocity of the flow.

In other words, my diagram is valid, isn't it?

 

[voko]

What exactly in your diagram is in agreement with #6?

 

[negation]

What exactly in your diagram is in agreement with #6?

You're right. I committed a careless blunder.

 

[voko]

Can you solve it now?

 

[negation]

Can you solve it now?

I presume this is in response to part (b) and that part (a) is correct.

As for part(b), I'm not too sure. The question is asking what significance is there if the velocity of the flow is > than the actual velocity. Is it even possible for any of the two lengths in a right angle triangle to be > than the hypotenuse?

 

[voko]

How can part (a) in #1 be correct, if it assumes that the effective velocity is the hypotenuse?

 

[negation]

How can part (a) in #1 be correct, if it assumes that the effective velocity is the hypotenuse?

Θ=arctan(v_river/v_effective)

 

[voko]

Is the effective speed known in advance?

 

[negation]

Is the effective speed known in advance?

Nope. It was not given. The questions I posted, as has been, were done so word for word.
Given the question, I tried solving it symbolically- part(a) can be done so. But part (b) makes no sense to me.

 

[voko]

Try to think logically. Imagine you are the skipper of that ferry. You need to find the angle given what you know. What would you know?

 

[negation]

Try to think logically. Imagine you are the skipper of that ferry. You need to find the angle given what you know. What would you know?

I do have v_actual, v_effective, v_river and right angle triangle. Is it possible to derive a numerical value in this case?

 

[voko]

Do you have the magnitude of v_effective?

 

[negation]

Do you have the magnitude of v_effective?

It was not given.

 

[voko]

I know it was not. You are the skipper, what do you know about your ferry and about your river?

 

[negation]

I know it was not. You are the skipper, what do you know about your ferry and about your river?

The question asked for an expression of an angle isn't it? Wouldn't arctan(v_river/v_effective) suffice as an expression?

 

[voko]

You said you copied the problem word for word. v_effective is not mentioned there.

 

[negation]

You said you copied the problem word for word. v_effective is not mentioned there.

I see where the confusion is.
V_effective was the variable I gave.
Otherwise, arcsin(v_river/v_actual) is equally a valid expression

 

[voko]

And what happens when v_river > v_actual?

 

[negation]

And what happens when v_river > v_actual?

I don't know. Assuming the triangle is a right angle triangle where v_effective is normal to v_river, then, v_actual is the hypothenuse. It does not make sense for the hypothenuse to be shorter than either of the other length.

 

[voko]

What does that mean? Can the ferry cross the river normally to the river if the flow speed is greater than the ferry's speed?

 

[negation]

What does that mean? Can the ferry cross the river normally to the river if the flow speed is greater than the ferry's speed?

It can't.

 

[voko]

Would that be an answer for part (b)?

 

[negation]

Would that be an answer for part (b)?

Yes. Would that suffice?

 

[voko]

I think so.