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

• Smartgurl
In summary, the problem deals with a ship's captain wanting to sail northeast while being influenced by a current with a velocity of 5.0km/h. The maximum speed of the ship is 30km/h. Using the equation Cos angle=A/H, the required heading of the ship is determined to be 80 degrees. The answer to the problem is [N 38 degrees E]. The direction of the current, south, is also given in the problem. Drawing a diagram and setting up equations using vector addition allows for the determination of the required heading without difficulty.
Smartgurl
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?

Cos angle=A/H

## The Attempt at a Solution

The answer is [N 38 degrees E]

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 :-)

## 1. What is relative motion?

Relative motion is the movement of an object in relation to another object. It is a concept used in physics to describe how an object's position, velocity, and acceleration change with respect to a reference point.

## 2. How is relative motion different from absolute motion?

Relative motion is different from absolute motion in that it takes into account the motion of one object with respect to another object, while absolute motion only considers an object's motion in relation to a fixed point, such as the ground.

## 3. What is the difference between relative velocity and relative acceleration?

Relative velocity is the rate at which the distance between two objects is changing, while relative acceleration is the rate at which the relative velocity is changing. In other words, relative acceleration is the change in relative velocity over time.

## 4. How do you calculate relative motion?

To calculate relative motion, you need to measure the position, velocity, and acceleration of each object and then determine the relative positions, velocities, and accelerations of the objects in relation to each other. This can be done using the principles of vector addition and subtraction.

## 5. What are some real-life examples of relative motion?

Some examples of relative motion in everyday life include a person walking on a moving train, a car passing another car on the highway, and a bird flying in the wind. In each of these scenarios, the object's motion is described relative to another object or reference point.

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