How Should a Ferryboat Navigate a River with Flowing Water?

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Homework Help Overview

The problem involves a ferryboat navigating a river with a current, requiring the determination of an angle to head in order to reach a town directly opposite. The subject area includes concepts from kinematics and vector analysis, particularly in the context of relative motion in fluid dynamics.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the relationship between the ferry's speed relative to the water and the river's flow speed, questioning how to express the angle needed for navigation. There are attempts to clarify the effective velocity and its direction, as well as the implications of the river's speed being greater than the ferry's speed.

Discussion Status

The discussion is ongoing, with participants exploring various interpretations of the problem. Some have offered insights into the effective velocity and its relationship to the ferry's navigation, while others are questioning the assumptions made regarding the triangle formed by the velocities.

Contextual Notes

Participants note that the effective speed of the ferry is not provided, leading to confusion in deriving expressions for the angle. There is also a focus on the implications of the river's speed exceeding the ferry's speed, raising questions about the feasibility of crossing the river directly.

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

Untitled.jpg
 
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?
 
voko said:
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
 
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.
 
voko said:
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?
 
What exactly in your diagram is in agreement with #6?
 
voko said:
What exactly in your diagram is in agreement with #6?

You're right. I committed a careless blunder.
Untitled.jpg
 
  • #10
Can you solve it now?
 
  • #11
voko said:
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?
 
  • #12
How can part (a) in #1 be correct, if it assumes that the effective velocity is the hypotenuse?
 
  • #13
voko said:
How can part (a) in #1 be correct, if it assumes that the effective velocity is the hypotenuse?

Θ=arctan(v_river/v_effective)
 
  • #14
Is the effective speed known in advance?
 
  • #15
voko said:
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.
 
  • #16
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?
 
  • #17
voko said:
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?
 
  • #18
Do you have the magnitude of v_effective?
 
  • #19
voko said:
Do you have the magnitude of v_effective?

It was not given.
 
  • #20
I know it was not. You are the skipper, what do you know about your ferry and about your river?
 
  • #21
voko said:
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?
 
  • #22
You said you copied the problem word for word. v_effective is not mentioned there.
 
  • #23
voko said:
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
 
  • #24
And what happens when v_river > v_actual?
 
  • #25
voko said:
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.
 
  • #26
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?
 
  • #27
voko said:
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.
 
  • #28
Would that be an answer for part (b)?
 
  • #29
voko said:
Would that be an answer for part (b)?

Yes. Would that suffice?
 
  • #30
I think so.
 

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