Problem involving displacement vectors

[frankfjf]

Alright, here's the problem:

A car is driven east for a distance of 41 km, then north for 27 km, and then in a direction 28° east of north for 26 km. Determine (a) the magnitude of the car's total displacement from its starting point and (b) the angle (from east) of the car's total displacement measured from its starting direction.

I'm not getting the right answer for part a, and I figure if part a is wrong, I'm going to have the same luck with part b.

From what I can tell, this problem is asking to obtain the total displacement by adding the vector components of each vector. I get the following numbers:

Vector 1: 41sin(0 degrees) = 0, 41cos(0 degrees) = 41

Vector 2: 27sin(90 degrees) = 27, 27cos(90 degreeS) = 0

Vector 3: 26sin(28) = 12.2, 26cos(28) = 23

Net X component: 41 + 0 + 23 = 64

Net Y component: 0 + 27 + 12.2 = 39.2

Then when I take the square root of 64^2 + 39.2^2 I get a wrong answer for the magnitude. What am I doing wrong?

 

[finchie_88]

Vector 3: 26sin(28) = 12.2, 26cos(28) = 23

I think it's this bit that's wrong, it says 28 degrees east of north (see diagram below - this is my intepretation), so using a little trig, does that not make the x-component 26sin28 and the y component 26cos28, then carry on as normal, and you should get the right answer.
| / Where the vertical line is north, and the angle A is 28 degrees.
| /
|A /
| /
|/

 

[quicknote]

I would suggest double checking your calculations and making sure you are using the correct units. In this problem, all distances are given in kilometers, so make sure you are using the appropriate trigonometric functions for that unit. Additionally, make sure you are using the correct angle for each vector. For example, for vector 3, the angle should be measured from north, not east.

Once you have double checked your calculations, you can use the Pythagorean theorem to find the magnitude of the total displacement. Remember to use the same units for both the x and y components.

For the second part of the problem, you can use the inverse tangent function to find the angle from east. This angle will be the inverse tangent of the y-component divided by the x-component. Make sure to convert the angle to the appropriate units (degrees or radians) based on the problem.

If you are still having trouble, I would suggest seeking help from a classmate or your instructor to review your calculations and ensure you are using the correct methods. It's important to be precise and accurate in scientific calculations.