Positions and vectors

  • Thread starter -EquinoX-
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In summary: Yes, that is correct. The problem does not state the angle explicitly, but based on the given directions (south, west, northwest), it can be assumed to be 45 degrees.
  • #1
-EquinoX-
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Homework Statement



A motorist drives south at 20.0 m/2 for 3.00 min, then turns west and travels at 25.0 m/s for 2 min, and finally travels northwest at 30.0 m/s for 1.00 min. For this 6.00 min trip, find (a) the total vector displacement, (b) the average speed, and (c) the average velocity.

Homework Equations





The Attempt at a Solution


Well I tried to convert all that to distance, so multiplying velocity and time. What I don't understand is the north east part. If I were to represent the first part. it would be 3600 m to the south, so -3600j and the second one would be -3000i to and what about the north east part?
 
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  • #2
-EquinoX- said:

Homework Statement



A motorist drives south at 20.0 m/2 for 3.00 min, then turns west and travels at 25.0 m/s for 2 min, and finally travels northwest at 30.0 m/s for 1.00 min. For this 6.00 min trip, find (a) the total vector displacement, (b) the average speed, and (c) the average velocity.

Homework Equations





The Attempt at a Solution


Well I tried to convert all that to distance, so multiplying velocity and time. What I don't understand is the north east part. If I were to represent the first part. it would be 3600 m to the south, so -3600j and the second one would be -3000i to and what about the north east part?

The problem says North West.

The length of the vector will be 1800 but the component vectors would be multiplied by (1/2)*sqrt(2).
 
  • #3
where did you get (1/2)*sqrt(2) from?
 
  • #4
-EquinoX- said:
where did you get (1/2)*sqrt(2) from?

That's the value of sine and cosine of a 45 degree angle. A right triangle of unit sides has a hypotenuse of sqrt(2). So finding the sine and cosine is simply 1/sqrt(2) or it can be written as (1/2)*sqrt(2).

You are going Northwest so the sine and cosine components of the displacement vector at that angle can be given as that.
 
  • #5
so if it says north west then you're assuming the angle is 45 degress with the x axis
 

1. What is the difference between position and vector?

Position refers to the location of an object in space, while vector refers to both the magnitude and direction of an object's movement.

2. How are positions and vectors represented mathematically?

Positions are represented by a set of coordinates, typically in the form (x,y,z), while vectors are represented by both a magnitude and direction, often denoted by an arrow above the vector symbol.

3. Can positions and vectors change over time?

Yes, both positions and vectors can change over time. Positions can change as an object moves in space, while vectors can change as an object's speed or direction changes.

4. What are some real-world applications of positions and vectors?

Positions and vectors are used in many fields, such as physics, engineering, and computer graphics. They are important in understanding the movement of objects, predicting trajectories, and designing efficient paths for robots.

5. How are positions and vectors used in navigation?

Positions and vectors are used in navigation to determine an object's location and direction of movement. GPS technology, for example, relies on positions and vectors to accurately track the position of a vehicle or person.

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