Vector Displacement Magnitude Calculation

In summary, a car drives 80.0 km west, turns southwest, and travels an additional 30.0 km. To find the displacement from the point of origin, the vector components can be determined using trigonometry. However, without given angles, the exact displacement cannot be found.
  • #1
kelli
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Homework Statement



After driving 80.0 km west, a car turns southwest and proceeds another 30.0 km. What is the displacement of the car from the point of origin (magnitude only)?


Homework Equations


The Attempt at a Solution



I tried drawing this out. I am given no angles, does this mean i add the vectors in head to tail fashion. or do i use trig and additon of vector components? please help. I am not asking for the answer just steps/explanations.
 
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  • #2
kelli said:

Homework Statement



After driving 80.0 km west, a car turns southwest and proceeds another 30.0 km. What is the displacement of the car from the point of origin (magnitude only)?


Homework Equations





The Attempt at a Solution



I tried drawing this out. I used trig to find out the x and y components. my resultant was 84 however the answer is wrong. I just don't know how to find the angles. I can do vector problems, but I've never done one without a given angle.

Welcome to the PF.

Please show us your work so we can find the error...
 

1. What are vector components?

Vector components refer to the individual parts or elements of a vector, which is a quantity that has both magnitude (size) and direction. In two-dimensional space, a vector typically has two components: one in the horizontal direction and one in the vertical direction. In three-dimensional space, a vector can have three components: one in the x-direction, one in the y-direction, and one in the z-direction.

2. How do you find the components of a vector?

To find the components of a vector, you can use trigonometric functions such as sine and cosine. For a two-dimensional vector, the horizontal component can be found by multiplying the magnitude of the vector by the cosine of the angle it makes with the x-axis. The vertical component can be found by multiplying the magnitude by the sine of the angle. For a three-dimensional vector, the x-component is found by multiplying the magnitude by the cosine of the angle it makes with the x-axis, and similarly for the y-component and z-component using the corresponding angles.

3. How do you represent vector components graphically?

In a two-dimensional graph, vector components can be represented as arrows on the x-axis and y-axis. The length of the arrow represents the magnitude of the component, and the angle it makes with the axis represents the direction. In a three-dimensional graph, vector components can be represented using a 3D coordinate system, with arrows along each axis representing the components.

4. Can vector components be negative?

Yes, vector components can be negative. A negative component indicates that the vector is pointing in the opposite direction of the positive component. For example, a vector with a negative vertical component would be pointing downwards instead of upwards. This is important to consider when performing vector operations such as addition or subtraction.

5. How are vector components used in physics?

In physics, vector components are used to represent physical quantities that have both magnitude and direction, such as force, velocity, and acceleration. By breaking these vectors into their components, it becomes easier to analyze and solve problems involving these quantities. Vector components are also used in vector operations, such as finding the resultant vector or resolving a vector into its components.

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