Vector Problem Homework: Finding Cyclist B's Route to Campground

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Cyclist A travels 1240m east and then 1600m north to reach the campground, while Cyclist B goes 1960m north but becomes lost. The task is to calculate the vector that will guide Cyclist B to the campground, including its magnitude and direction. The proposed solution indicates that Cyclist B must travel 1291m at an angle of 16.19° South of East. Feedback from peers confirms that this calculation appears correct.
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Homework Statement


Two cyclists, A and B, start off traveling to a campground. Cyclist A travels due east for 1240m, then turns north and travels for 1600m, ending at the campground.
Cyclist B starts off going north for 1960m, then stops, confused and lost, and asks for directions. Calculate the vector that will take cyclist B to the campground, specifying both magnitude and direction.


Homework Equations





The Attempt at a Solution


I've attached an image of my attempt. I'm not sure if it's correct or not. If someone could take a look at it and point me in the right direction, I'd really appreciate it! My final answer is that the cyclist must travel 16.19° South of East for 1291 m, but I really want to make sure my process is correct.
 

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theintarnets said:

Homework Statement


Two cyclists, A and B, start off traveling to a campground. Cyclist A travels due east for 1240m, then turns north and travels for 1600m, ending at the campground.
Cyclist B starts off going north for 1960m, then stops, confused and lost, and asks for directions. Calculate the vector that will take cyclist B to the campground, specifying both magnitude and direction.

Homework Equations



The Attempt at a Solution


I've attached an image of my attempt. I'm not sure if it's correct or not. If someone could take a look at it and point me in the right direction, I'd really appreciate it! My final answer is that the cyclist must travel 16.19° South of East for 1291 m, but I really want to make sure my process is correct.
That looks fine to me !
 

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