Vector magnitude and displacement

In summary, the problem involves a car traveling east for 48 km, then north for 25 km, and then 25° east of north for 28 km. The total displacement of the car from its starting point can be determined using the formula A^2=Ax^2 + Ay^2, taking into account the contributions of all three distances. To do this, the 28 km distance can be broken down into its east and north components and added to the other components. This will result in an x component of 48+28sin25 and a y component of 25+28cos25. Using the Pythagorean theorem, the overall displacement can be calculated. It is important to not simply plug values into a
  • #1
jpd5184
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0

Homework Statement



A car is driven east for a distance of 48 km, then north for 25 km, and then in a direction 25° east of north for 28 km. Draw the vector diagram and determine the total displacement of the car from its starting point.

whats the magnitude and direction(counterclockwise from east)


Homework Equations



A^2=Ax^2 + Ay^2


The Attempt at a Solution



i plugged in 48km for Ax and 25km for Ax and got 82.103km for my answer
 
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  • #2
you seem to be missing the contributions of the 28 km. Draw the diagram and attach it.
 
  • #3
i noticed that the 28km was left out, i drew it on my picture but I am not sure what forumula to use to utilize it.
 
  • #4
Are you able to break down the 28 km into its east and north components? If you can do that, then add all the east components together, and then ... can you do it now?
 
  • #5
do you mean like:

x= 28cos25
y= 28cos65
 
  • #6
yes, except I think your angles should be interchanged. Then to get the overall displacement you have an x component of 48+28sin25 and a y component of ... Then use pythagoras on the two overall components. In future, try to not think of 'plugging into a formula' without thinking what it means.
 

1. What is the difference between vector magnitude and displacement?

Vector magnitude refers to the numerical value or size of a vector, while displacement refers to the change in position of an object or particle. Vector magnitude is a scalar quantity, meaning it has only magnitude and no direction, while displacement is a vector quantity, meaning it has both magnitude and direction.

2. How do you calculate the magnitude of a vector?

To calculate the magnitude of a vector, you can use the Pythagorean theorem, which states that the length of the hypotenuse of a right triangle (the magnitude) is equal to the square root of the sum of the squares of the other two sides (the components of the vector).

3. Can the magnitude of a vector be negative?

No, the magnitude of a vector is always a positive value. It represents the size or length of the vector, so it cannot be negative.

4. How is displacement represented in a vector diagram?

Displacement is represented by an arrow in a vector diagram, with the length of the arrow representing the magnitude and the direction of the arrow indicating the direction of displacement.

5. Can vector magnitude and displacement be equal?

No, vector magnitude and displacement are two different quantities and can have different values. Vector magnitude refers to the size or length of the vector, while displacement refers to the change in position. However, in some cases, the magnitude of a vector may be equal to the displacement if the vector is a straight line and there is no change in direction.

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