# Course and Ground Speed (Navigation problem)

• Elidibz
In summary, to find the course and ground speed of a plane flying at 120 degrees with an air speed of 300mph and facing a 40mph wind blowing north to south, you can use the law of cosines and law of sines to find the third side and one of the remaining angles in the triangle formed by the plane's direction and the wind's vector. The final velocity of the plane is the sum of the two vectors.
Elidibz

## Homework Statement

A plane flies in the direction 120 degrees with an air speed of 300mph. The wind is blowing north to south at 40mph. Find the course and ground speed of the plane.

## The Attempt at a Solution

I attempted this problem, but i still cannot figure out how we get the second angle?

Have you drawn a picture?
Do you know how to decompose vectors into their components? If you don't know how to work with vectors, your picture should help you get the largest angle in the triangle formed by the plane's direction vector and the wind's vector. You know two of the sides of the triangle and the angle between them, so you can use the law of cosines to find the third side of the triangle. After you have found it, you can use the law of sines to find one of the remaining angles in the triangle.

Draw the vectors as suggested. The final velocity of the airplane is the sum of the two vectors.

## 1. What is course and ground speed in navigation?

Course and ground speed are two important measures used in navigation to determine the speed and direction of an aircraft or vessel. Course refers to the direction of travel relative to a fixed point, while ground speed is the actual speed at which the aircraft or vessel is moving over the ground.

## 2. How is course and ground speed calculated?

Course and ground speed are calculated using a combination of instruments and mathematical calculations. The course can be determined using a compass or heading indicator, while ground speed is calculated by measuring the time it takes to travel between two known points and using the distance between them.

## 3. What factors can affect course and ground speed?

Course and ground speed can be affected by a number of factors including wind speed and direction, altitude, and the weight and aerodynamics of the aircraft or vessel. These factors must be taken into account when calculating and adjusting course and ground speed for accurate navigation.

## 4. Why is it important to know course and ground speed during navigation?

Knowing the course and ground speed is crucial for pilots and sailors to accurately navigate to their destination. By constantly monitoring these measures, they can make adjustments to account for changing conditions and ensure they are on the right path to reach their destination safely and efficiently.

## 5. Can course and ground speed be affected by the Earth's rotation?

Yes, the Earth's rotation can have a slight effect on course and ground speed. This is known as the Coriolis effect, which causes objects in motion to follow a curved path due to the rotation of the Earth. However, this effect is generally only noticeable over long distances and is taken into account in navigation calculations.

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