How to solve for vectors components

[warnexus]

Homework Statement

A car drives north at 48mi/h for 10 min and then turns east and goes 5.0 mi at 66mi/h . Finally, it goes southwest at 36mi/h for 6.0 min.

Determine the car's displacement.

Assume that the positive x and y axes are directed to the east and north, respectively.
Answers should be in x and y components of the resultant

Homework Equations

x component aka i hat lies in the x-axis
y component aka j hat lies in the y axis

The Attempt at a Solution

since the car is going north at that velocity. the magnitude of that vector is 8 mi. When the car goes east, the magnitude is given as 5.0mi. when the car moves southwest, the magnitude is 3.6mi.

Not sure if the graph is right but I thought I get feedback on it.

 

[Norfonz]

The total displacement is merely the sum of the given vectors. Write each vector in terms of its components. Note that a direction like southwest implies a 45 degree angle between south and west, this should help you write the components.

To find a vector component in a direction, you need to know the angle between the vector and that direction.

 

[Naty1]

since the car is going north at that velocity. the magnitude of that vector is 8 mi. When the car goes east, the magnitude is given as 5.0mi. when the car moves southwest, the magnitude is 3.6mi.

correct...

so plot these on graph paper, tail to head [ector arrow point], and connect the final head to the origin...the length is your final magntiude and the angle you measure relative to horizontal records the orientation. ..so for example, go 8 up [vertical], from there 5 down and to the right at 45 degrees 5, then horizontal right from there 3.6...

 

[warnexus]

I thought it was 5 horizontal right and 3.6 down left. Thanks for the feedback. i added a picture on what I did with the vector components. I feel super stuck on this problem.

 

[Nickie]

I would like to point out that the given information is incomplete. In order to solve for the car's displacement, we also need to know the starting point of the car's journey. Without this information, we cannot accurately determine the displacement in terms of x and y components.

Assuming that the starting point is the origin (0,0), we can use the given information to calculate the displacement. The car's displacement can be represented as a vector with its tail at the origin and its head at the final position of the car.

To calculate the x and y components of the displacement, we can use the following equations:

x component = magnitude of displacement * cos(theta)
y component = magnitude of displacement * sin(theta)

In this case, the magnitude of displacement can be calculated by adding the magnitudes of the individual vectors (8 mi, 5.0 mi, and 3.6 mi) and the angle theta can be determined by using trigonometry.

Therefore, the x component of the displacement would be 8 mi + 5.0 mi * cos(theta) and the y component would be 5.0 mi * sin(theta) - 3.6 mi.

I would also like to suggest that instead of using a graph, it would be more accurate to use vector addition to calculate the displacement. This involves drawing the individual vectors to scale and using the parallelogram method to determine the resultant vector, which represents the displacement of the car.