Calculating the sum of displacement vectors

[student120]

Homework Statement

No, I'm trying to learn.

Relevant Equations

Vector 1: V1=(0,100)
Vector 2: V2=(100,0)
Vector 3: V3=(0,-300)
Vector 4: V4=(-150,0)
Vector 5: V5=(-200cos(60°),-200sin(60°))
but after that I couldn't go any further

I greet everyone

I am faced with such a question

First 100m to the right, then 300m down, then 150 left diagonally, even I don't think this is exactly right, I think there will be 150x sin30 or cos30, but I'm not sure, I need to do 200xcos60 afterwards, but I couldn't settle the question. can anyone help me solve it step by step?

Every answer from the community will be honored, thanks in advance

 

[phinds]

can anyone help me solve it step by step?

No, what we CAN do, based on forum rules, is show you where you are going wrong once you show YOUR step by step analysis. We don't spoon feed answers, we help you figure out how to get your own answers.

 

[kuruman]

Consider a step-by-step analysis where you write down 4 displacement vectors which is what your diagram shows. The attempt at it that you posted under "Relevant Equations" is not correct and shows 5 vectors whereas you have 4. Please try again.

 

[haruspex]

Vector 1: V1=(0,100)

Where is that in the diagram?

Vector 2: V2=(100,0)
Vector 3: V3=(0,-300)

ok

Vector 4: V4=(-150,0)
Vector 5: V5=(-200cos(60°),-200sin(60°))

No and no.
Use the same approach in 4 that you appear to have used in 5, but be careful with the signs.

 

[jtbell]

And for “Vector 5” (which is actually the 4th vector in the chain), you show both x and y components as negative. According to your diagram, that vector points to the left, which is indeed the negative x direction, and upward, which is the ___?___ y direction.

 

[Gavran]

can anyone help me solve it step by step?

There are three steps.
The help for the first step is the post #4.
The help for the second step is https://en.wikipedia.org/wiki/Euclidean_vector#Addition_and_subtraction.
The help for the third step is https://en.wikipedia.org/wiki/Inverse_trigonometric_functions#Finding_the_angle_of_a_right_triangle.