# Waterboat Question -- which heading to take....

• isthistakenyet
isthistakenyet

## Homework Statement

If you were trying to cross a river with the shortest possible time, would you aim your boat slightly upstream, directly across the river, or slightly downstream? Explain.

w = water
s = shore
b = boat

## The Attempt at a Solution

I thought about this question but I'm not sure if I should take distance into account. Because, technically, while the velocity for downstream is the greatest, doesn't the distance increase? As you can see in the picture, it looks like they will all take the same amount of time because the distance keeps increasing.

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isthistakenyet said:

## Homework Statement

If you were trying to cross a river with the shortest possible time, would you aim your boat slightly upstream, directly across the river, or slightly downstream? Explain.

w = water
s = shore
b = boat

## The Attempt at a Solution

I thought about this question but I'm not sure if I should take distance into account. Because, technically, while the velocity for downstream is the greatest, doesn't the distance increase? As you can see in the picture, it looks like they will all take the same amount of time because the distance keeps increasing.

Welcome to the PF.

The problem asks for the path with the shortest possible time shore-to-shore, not caring about the distance traveled. One important Relevant Equation is for the component of velocity in the horizontal direction shore-to-shore. How is that component of velocity related to the absolute velocity of the boat and the angle it is inclined above or below the horizontal?

berkeman said:
Welcome to the PF.

The problem asks for the path with the shortest possible time shore-to-shore, not caring about the distance traveled. One important Relevant Equation is for the component of velocity in the horizontal direction shore-to-shore. How is that component of velocity related to the absolute velocity of the boat and the angle it is inclined above or below the horizontal?
But wouldn't the distance traveled increase the time it takes?

isthistakenyet said:
But wouldn't the distance traveled increase the time it takes?

Write out the equation I alluded to, and you can then tell me...

berkeman said:
Write out the equation I alluded to, and you can then tell me...
but how exactly would the component affect the time it takes, sorry I'm not very good at physics. And how do I write an equation for the component if I haven't been given any info? sorry for noobyness.

isthistakenyet said:
but how exactly would the component affect the time it takes, sorry I'm not very good at physics. And how do I write an equation for the component if I haven't been given any info? sorry for noobyness.

No need to be sorry. Call the speed of the boat V. If the boat aims directly across the river (call it horizontal or x on the drawing), then Vx = V.

But if the boat aims above or below the horizontal by an angle θ then you should be able to write equations for Vx and Vy in terms of V and a trig function of θ. What are Vx and Vy in terms of θ?

This is a trick question, is it not?

Note that the boat's "speed" is it's velocity with respect to the water that it travels across. If the boat's "speed" is zero, then it moves downstream at the same speed as the water (ignoring issues like drag from the air).

Last edited:
Another approach is to use the reference frame of the water.

DaveC426913 said:
This is a trick question, is it not?

Without giving away the solution, can you say why it seems like a trick question?

berkeman said:
Without giving away the solution, can you say why it seems like a trick question?
Well, I think almost everyone seems to be in agreement that the answer is simpler than it seems.

berkeman
DaveC426913 said:
Well, I think almost everyone seems to be in agreement that the answer is simpler than it seems.
So far, only OP seems to have a problem getting the solution.

Well, the answer turned out to be straight across :/

isthistakenyet said:
Well, the answer turned out to be straight across :/

isthistakenyet

## 1. What is the "Waterboat Question" about?

The "Waterboat Question" is a hypothetical scenario that involves a boat on a body of water with uncertain currents and winds. The question asks which heading the boat should take to reach its destination in the most efficient way.

## 2. Why is this question important?

This question is important because it highlights the complexity of navigation and decision-making in uncertain environments. It also demonstrates the importance of understanding factors such as currents and winds when navigating on water.

## 3. Is there a right answer to the "Waterboat Question"?

No, there is not necessarily a "right" answer to the Waterboat Question as it depends on various factors such as the specific conditions of the body of water and the capabilities of the boat. However, there are strategies and techniques that can be used to make an informed decision.

## 4. What are some possible approaches to solving the "Waterboat Question"?

One approach is to gather information about the currents, winds, and other environmental factors to determine the most favorable heading. Another approach is to use navigational tools and instruments to aid in decision-making. Additionally, experience and knowledge of sailing and navigation can also play a role in solving this question.

## 5. How can the "Waterboat Question" be applied in real-life situations?

The "Waterboat Question" can be applied in various real-life situations such as sailing, boating, and other forms of water transportation. It can also serve as a thought exercise for decision-making in uncertain environments and can be used to teach navigation principles and strategies.

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