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It looks like you've already started sketching the vector diagram in your image, which is a great start! Your sketch correctly shows the three displacement vectors and the resultant total displacement
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4 stepsIt looks like you've already started sketching the vector diagram in your image, which is a great start! Your sketch correctly shows the three displacement vectors and the resultant total displacement.
Here's a detailed breakdown of the solution:
Part a
Sketch the vector diagram
Your sketch accurately represents the three displacement vectors:
- A vector of 50 km pointing East (along the positive x-axis).
- A vector of 30 km pointing North (along the positive y-axis), starting from the end of .
- A vector of 25 km at East of North, starting from the end of . This means the angle is measured from the North axis towards the East.
- The resultant total displacement vector, , drawn from the origin (start of ) to the end of .
Part b
Determine the total displacement of the car
Resolve each displacement vector into its East (x) and North (y) components.
Let East be the positive x-direction and North be the positive y-direction.
For :
For :
For :
The angle is with respect to the North axis.Sum the x-components and y-components to find the total displacement components.
Total East displacement ():
Total North displacement ():
Calculate the magnitude of the total displacement.
The magnitude is found using the Pythagorean theorem:
Calculate the direction of the total displacement.
The direction is found using the arctangent function, measured from the East axis towards the North:
Since both and are positive, the direction is North of East.
The total displacement of the car is .
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