Why Is My Vector Calculation Incorrect?

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To solve the vector problem of a car traveling 20 km north and 35 km at 60 degrees west of north, it's essential to resolve the vectors into their north and west components. The initial calculations yielded a magnitude of 40.1 km, but the correct answer is 48 km, indicating a misunderstanding in vector resolution. The components must be treated as perpendicular, which is crucial for applying the vector equation correctly. By accurately calculating the north and west components and then using them in the vector equation, the correct magnitude and direction can be determined. Understanding vector components is key to resolving such problems effectively.
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How to solve this vector problem?

Homework Statement



A car travels 20 km due north and then 35 km in a direction of 60degree west of north. Find the magnitude and direction of a single vector that gives the net effect of the car trip.

Homework Equations



(vector) R = square root (vector)( A^2 + B^2)

The Attempt at a Solution



I found the answer is 40.1 km while the answer says it's 48 km. I don't know how to solve the angle. Help please!
 
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sowmit said:

Homework Statement



A car travels 20 km due north and then 35 km in a direction of 60degree west of north. Find the magnitude and direction of a single vector that gives the net effect of the car trip.

Homework Equations



(vector) R = square root (vector)( A^2 + B^2)

The Attempt at a Solution



I found the answer is 40.1 km while the answer says it's 48 km. I don't know how to solve the angle. Help please!
Try resolving the vectors into their North and West components and adding the components. Then find the length from these perpendicular components.

AM
 


Solve their north and west component? How is that possible? Isn't that given in the problem already?
 


What Andrew Mason is saying is that the components given in the problem are not perpendicular; this is the reason your equation is not working. Try making two perpendicular components, one north and one west (not at an angle west). Then use these in the equation.
 
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