Calculating Displacement: Understanding Vectors in Physics

In summary: You have two sides and the included angle. You can use the cosine rule to find the third side. In summary, the car's displacement can be found using the Pythagorean theorem and the cosine rule. It traveled 10 km due EAST and 12 km NW, and the magnitude of its displacement is 8.6 km. The third side of the triangle can be found by applying the cosine rule, which states that c^2 = a^2 + b^2 - 2ab*cosA. However, the angle's value is still unknown and can be found by drawing a diagram and using the cosine rule.
  • #1
Said90
3
0
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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  • #2
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.
 
  • #3
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?
 
  • #4
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?
 
  • #5
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
 
  • #6
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.
 

Related to Calculating Displacement: Understanding Vectors in Physics

1. What is displacement in physics?

Displacement is the distance and direction of an object's change in position from its starting point to its ending point. It is a vector quantity that takes into account both magnitude (distance) and direction.

2. How do you calculate displacement?

To calculate displacement, you need to know the initial position (x1) and final position (x2) of the object. The formula for displacement is:
Δx = x2 - x1

3. Can displacement be negative?

Yes, displacement can be negative. The negative sign indicates that the object has moved in the opposite direction of the chosen positive direction. For example, if the chosen positive direction is to the right, then a displacement of -5 meters means that the object has moved 5 meters to the left.

4. How is displacement different from distance?

Distance is a scalar quantity that only takes into account the total length traveled, while displacement is a vector quantity that includes both distance and direction. Distance is always positive, while displacement can be positive, negative, or zero.

5. What is the difference between displacement and velocity?

Displacement is the change in position of an object, while velocity is the rate of change of displacement over time. Velocity is a vector quantity that takes into account both the speed and direction of an object's motion.

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