Using Vectors to Find Displacement and Angle

In summary, the person walked a total distance of 8.6 km in a north, west, and south pattern. To determine the distance and angle of a bird flying in a straight line from the starting point to the final point, one can create triangles for each direction and use basic trigonometry to find the values of the x and y components. The final triangle can then be created using the sum of all x and y components, and the displacement value can be determined using the Pythagorean Theorem. The angle can be found by using the inverse of tangent. A drawing can also be helpful in visualizing the problem.
  • #1
sb13
22
0

Homework Statement


A person walks in the following pattern: 4.1 km north, then 2.0 km west, and finally 2.5 km south.

Homework Equations


(a) How far (in km) and (b) at what angle (measured counterclockwise from east) would a bird fly in a straight line from the same starting point to the same final point?

The Attempt at a Solution


I know that I need to create the triangles for 4.1, 2.0, and 2.5, and use basic trigonometry (sine and cosine) to find the values of each of their x and y components, but I am not sure which reference angles to use 30 degrees, 60 degrees, 45 degrees? How am I supposed to tell? I know where to go from there, you add up all of the x components, and then all of the y components, and then create your final triangle and determine the displacement value using the Pythagorean Theorem. Then you determine the angle by using the inverse of tangent.
I just need help with determining the angles for those three triangles.
 
Physics news on Phys.org
  • #2
Hi sb13,

Make a drawing. Everything will be simple.

ehild
 
  • #3
Thank you. I figured it out.
 

FAQ: Using Vectors to Find Displacement and Angle

What is a vector?

A vector is a mathematical representation of a physical quantity that has both magnitude and direction. It is typically denoted by an arrow, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction.

How do you calculate the magnitude of a vector?

The magnitude of a vector can be calculated using the Pythagorean theorem. It is the square root of the sum of the squares of the components of the vector. For example, if a vector has components x and y, its magnitude would be √(x² + y²).

What is displacement?

Displacement is a vector quantity that represents the shortest distance and direction from the starting point to the final position of an object. It is different from distance, which is a scalar quantity that represents the total length of the path traveled by an object.

How do you use vectors to find displacement?

To find displacement, you would need to add all the individual vectors that represent the different movements of the object. The result would be the resultant vector, which represents the displacement of the object.

How do you use vectors to find angle?

To find the angle between two vectors, you can use the dot product formula: a · b = |a| |b| cos θ, where a and b are the two vectors and θ is the angle between them. You can solve for θ by rearranging the formula to cos θ = (a · b) / (|a| |b|) and then using the inverse cosine function on your calculator to find the angle.

Similar threads

How to find d2 when given d1 and d, total time, and average velocity?
Replies
1
Views
2K
Overall displacement vector from a walking trip....
Replies
19
Views
7K
Map question involving vectors (find the angle)
Replies
13
Views
2K
Displacement -0.25i + 14.7j from Origin: Final Displacement
Replies
4
Views
1K
Find the magnetic induction vector
Replies
3
Views
444
Find angle between displacement and velocity vector
Replies
3
Views
4K
Vectors: Displacement, average velocity & speed
Replies
7
Views
2K
Calculate electric force using Coulomb's law (vector components are the struggle)
Replies
3
Views
584
Torque on a Circular Current Loop under a Misaligned Magnetic Field
Replies
1
Views
484
Net Displacement: Calculate x,y & r,θ
Replies
7
Views
3K

Hot Threads

Recent Insights

Back
Top