Calculating Required Heading for North-East Sailing with Current at 5km/h

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Homework Help Overview

The problem involves a ship's captain attempting to navigate north-east while contending with a current moving at 5.0 km/h. The ship's maximum speed is given as 30 km/h, and the goal is to determine the required heading to achieve the desired course.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the necessity of knowing the current's direction to solve the problem effectively. There are suggestions to draw a diagram and to use vector addition to analyze the ship's velocity relative to the water and the current.

Discussion Status

The discussion is active, with participants exploring different interpretations of the problem and suggesting methods for approaching the solution. Some guidance has been offered regarding the use of diagrams and equations, but no consensus has been reached on a specific method.

Contextual Notes

There is a mention of the current moving south, which may influence the calculations and assumptions being discussed. Participants are also considering the implications of the ship's heading and effective velocity.

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Homework Statement


A ships captain wishes to sail his ship north -east. A current is moving his ship with a velocity of 5.0km/h . If the ship has a maximum speed of 30 km/h what is the ships required heading?

Homework Equations


Cos angle=A/H

The Attempt at a Solution


Heading=cosine (5/30)
Heading=80 degrees
The answer is [N 38 degrees E]
 
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Just out of curiosity, are you given the direction in which the current is moving his ship?
Edit: maybe I'm mistaken, but I feel like you need that information to solve this problem..
 
_N3WTON_ said:
Just out of curiosity, are you given the direction in which the current is moving his ship?
Edit: maybe I'm mistaken, but I feel like you need that information to solve this problem..
Yes it says south.
 
Ok, for problems like these it is essential to draw a diagram. You are trying to find the angle the ship is making with the x-axis (east axis). First you will need to set up an equation using the Pythagorean theorem, try that out as a start...
 
So the vector addition of ship's velocity wrt water + velocity of water = effective velocity of ship, right ?
Write out the components in direction north and in direction east to get two equations with two unknowns (heading wrt water and effective speed). You don't need the latter, so eliminate it. I see the answer appearing without any difficulty ...

Oh, and: welcome to PF :-)
 

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