Solving Vector Components: East-West and North-South Directions

[mandi182]

Vectors (HELP!)

Homework Statement

Consider a map oriented so that the x-axis runs east*west (with east being the “positive” direction), and y runs north*south (with north “positive”). A person drives 47 km to the west, then turns and drives 156 km towards the south.

Find x and y components

Homework Equations

The Attempt at a Solution

I have no idea how to solve this, I having been trying for 3 hours! I am not sure how to start.

Thanks!

 

[PhanthomJay]

I think your question is to find the x and y components of the resultant displacement. Is that the entire question? Start by drawing a sketch. The answer may be staring you in the face.

 

[f24u7]

This is a relatively easy question,

if x = the line of east and west than a person that drives west is also driving in the x direction

if y = the line of north and south than a person that drives south is also driving in the y direction

i think that's enough clue, now figure the signs by yourself

 

[mandi182]

Thanks, I figured it out. It was really easy and it really was staring me in the face!

 

[rwisz]

I understand that solving vector components can be a challenging task. However, with the right approach, it can be easily solved. In this case, we have a person who drives 47 km to the west and then turns and drives 156 km towards the south. This can be represented as a vector with an initial point at the starting point and a terminal point at the final destination.

To solve for the x and y components, we can use basic trigonometric principles. Since the person drove to the west, we can represent this as a negative value on the x-axis. Similarly, since the person drove towards the south, we can represent this as a negative value on the y-axis. Therefore, the x-component would be -47 km and the y-component would be -156 km.

To find the magnitude and direction of this vector, we can use the Pythagorean theorem and inverse trigonometric functions. The magnitude can be calculated as √(x^2 + y^2), which in this case would be √(47^2 + 156^2) = 161.96 km. The direction can be calculated as tan^-1(y/x), which in this case would be tan^-1(-156/-47) = 73.5° south of west.

I hope this explanation helps in understanding how to solve vector components in the east-west and north-south directions. Remember to always break down the problem into smaller components and use basic trigonometric principles to solve for the x and y components. Good luck!