Stuck on vector addition and subtraction

In summary, the person is seeking help with two math problems. The first problem involves finding the angle for a boat to move straight across a river at a given speed and flow rate. The second problem involves calculating a plane's velocity over the ground based on its bearing and cross wind speed. The person does not know how to solve these problems and is asking for assistance.
  • #1
victorhugo
127
5
Hello, here is a couple of example problems I'm not sure how to do, if someone could please explain how to do it I would greatly appreciate it!

Subtraction:
"A river flows at 0.8 m/s. If a boat moves across the water at 2m/s at what angle should it point so that it moves straight across the river perpendicular to the bank?"

Addition:
"A plane flies at a bearing of 270 degrees at 200km/h through a cross wind blowing from a bearing of 360 degrees at 80km/h. What is the plane's velocity over the ground?"

Thank you!
 
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  • #2
You have to at least make an attempt to answer the questions.
 
  • #3
I actually don't know what to do... the only way I learned is to get the displacement by using Pythagoras theorem, then diving that by the time to get the average velocity, so that's why I'm asking if someone could tell me what to do here :/
 
  • #4
Take one of your problems, and use the procedure you know on it. Show your work. Then people here can help you.
 

Related to Stuck on vector addition and subtraction

1. What is vector addition and subtraction?

Vector addition and subtraction is the mathematical process of combining or separating vectors, which are quantities that have both magnitude and direction. This process is used to determine the net displacement or force of multiple vectors acting on an object.

2. How do I perform vector addition and subtraction?

To add or subtract vectors, you must first determine their components (magnitude and direction) and then use the appropriate equations to combine or separate them. You can use graphical methods, such as the head-to-tail method, or algebraic methods, such as using vector components and the Pythagorean theorem.

3. What are some real-world applications of vector addition and subtraction?

Vector addition and subtraction have many applications in physics, engineering, and other scientific fields. For example, they are used in navigation to determine the resultant velocity of a moving object, in construction to calculate the forces acting on a structure, and in mechanics to analyze the motion of objects under the influence of multiple forces.

4. What are some common mistakes when working with vector addition and subtraction?

One common mistake is forgetting to include the direction of a vector when performing mathematical operations, resulting in incorrect solutions. Another mistake is not properly breaking down vectors into their components, leading to incorrect calculations. It is also important to be aware of the difference between vector addition and scalar addition, where the latter simply adds magnitudes and does not consider direction.

5. Are there any shortcuts or tips for solving vector addition and subtraction problems?

One useful tip is to draw accurate and clear diagrams to visualize the vectors involved and their relative positions. This can help in determining the correct direction and magnitude of the resultant vector. Additionally, it is helpful to break down complex vectors into simpler ones and deal with them separately before combining them back together. Practice and familiarity with vector operations can also help in solving problems more efficiently.

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