Vector Diagram Question: Finding Resultant Displacement using Components

In summary, a vector diagram question involves using vectors to represent physical quantities. To draw a vector diagram, you determine the magnitude and direction of the vector and draw an arrow with the correct proportions. The purpose of a vector diagram is to visually represent a vector's magnitude and direction. It can have any number of vectors and is used to understand the relationship between different vectors. To calculate the resultant vector in a vector diagram, you use vector addition and trigonometry.
  • #1
joe215
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Homework Statement



A disoriented bird flies 5.18 km east, then 6.2 km north, and then 2.05 km west. What is the magnitude and direction of the resultant displacement? (using the method of components)

The Attempt at a Solution



When I draw a diagram, the resulting figure is a trapezoid. Should I just find the missing side and angle using the pythagorean theorem and trig functions?
 
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  • #2


You could, but why don't you solve it as instructed, using the method of components. That will be really easy.
 
  • #3


Yes, that is correct. To find the resultant displacement using the method of components, you will need to use the Pythagorean theorem to find the magnitude of the resultant displacement and trigonometric functions to find the direction. The bird's final position can be represented by the diagonal of the trapezoid, which is the resultant displacement. By breaking down the bird's movements into east and north components, you can use these components to form a right triangle and apply the Pythagorean theorem to find the magnitude of the resultant displacement. Then, you can use trigonometric functions to find the direction of the resultant displacement. I would recommend labeling the trapezoid's sides and angles as well as the components and the resultant displacement to clearly visualize and solve the problem.
 

FAQ: Vector Diagram Question: Finding Resultant Displacement using Components

What is a vector diagram question?

A vector diagram question is a type of problem that involves the use of vectors to represent physical quantities. This can include forces, velocities, accelerations, and other quantities that have both magnitude and direction.

How do you draw a vector diagram?

To draw a vector diagram, you first need to determine the magnitude and direction of the vector. Then, draw an arrow to represent the vector, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction of the vector. The tail of the arrow should be placed at the starting point of the vector.

What is the purpose of a vector diagram?

The purpose of a vector diagram is to visually represent the magnitude and direction of a vector. This can help in solving problems involving vector addition, subtraction, and other operations, as well as in understanding the relationship between different vectors in a system.

Can a vector diagram have more than two vectors?

Yes, a vector diagram can have any number of vectors. In some cases, multiple vectors may be acting on an object or system at the same time, and a vector diagram can help in understanding the overall effect of these vectors.

How do you calculate the resultant vector in a vector diagram?

To calculate the resultant vector in a vector diagram, you need to use vector addition. This involves finding the sum of the individual components of the vectors in the x and y directions. The magnitude of the resultant vector can be found using the Pythagorean theorem, and the direction can be determined using trigonometric functions.

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