Calculating Displacement: Understanding Vectors in Physics

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A car travels 10 km due east and then 12 km northwest, leading to a displacement calculation. The correct magnitude of the car's displacement is determined to be 8.6 km, as clarified after initial confusion with the book's answer of 8.8 km. The Pythagorean theorem was incorrectly applied since the triangle formed is not right-angled. Participants suggest using the cosine rule to find the third side of the triangle, emphasizing the need for the angle between the two vectors. Drawing a diagram is recommended to visualize the problem better.
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A car travels 10 km due EAST then 12. Km NW what is Magnitude of the car's displacement.

The answer that I got in my book is 8.8
Could anyone-please-explain ?

The Attempt at a Solution


6.6 km[/B]
 
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Said90 said:
A car travels 10 km due EAST then 12. Km NW what is Magnitude of the car's displacement.

The answer that I got in my book is 8.8
Could anyone-please-explain ?

The Attempt at a Solution


6.6 km[/B]
I got 8.6. We can't tell where your mistake is until you post your working.
 
haruspex said:
I got 8.6. We can't tell where your mistake is until you post your working.

***I made a mistake .. The answer in the book is 8.6***I've just applied Pythagorean theorem to get the answer !
144 = 100+X^2

Could please explain your answer?
 
Said90 said:
***I made a mistake .. The answer in the book is 8.6***I've just applied Pythagorean theorem to get the answer !
144 = 100+X^2

Could please explain your answer?
It is not a right-angled triangle. Do you know a rule for finding the third side of a triangle given two sides and the angle between them?
 
haruspex said:
It is not a right-angled triangle. Do you know a rule for finding the third side of a triangle given two sides and the angle between them?

Yea..I got the idea

C^2=a^2+b^2- 2bc COSa
But still don't know how to get the angle's value
 
Said90 said:
Yea..I got the idea

C^2=a^2+b^2- 2bc COSa
But still don't know how to get the angle's value
Draw yourself a diagram.
 

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