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

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SUMMARY

The discussion focuses on calculating the required heading for a ship sailing north-east while being affected by a current moving at 5.0 km/h to the south. The ship's maximum speed is 30 km/h. The correct heading is determined to be 80 degrees, which translates to a navigational direction of N 38 degrees E. The solution involves vector addition and the Pythagorean theorem to account for the current's influence on the ship's trajectory.

PREREQUISITES
  • Understanding of vector addition in physics
  • Knowledge of the Pythagorean theorem
  • Familiarity with trigonometric functions, specifically cosine
  • Ability to interpret navigational headings
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  • Study vector addition in navigation scenarios
  • Learn about the Pythagorean theorem applications in physics
  • Explore trigonometric functions and their applications in real-world problems
  • Research navigational techniques for sailing under current influences
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Maritime navigators, physics students, and anyone involved in sailing or navigation who needs to calculate headings under the influence of currents.

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OP warned about not including efforts to solve the problem

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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