Solve Displacement Vectors Homework

• EL ALEM
In summary, the hiker's route consisted of displacement vectors A, B, C with known and unknown lengths and directions. Using the sine law, the unknown lengths of B and C were found to be approximately 5548.6477 m and 6158.829 m, respectively. These values were confirmed to be correct.
EL ALEM

Homework Statement

Route follewed by hiker consists of displacement vectors A, B, C. Vector A is 1550 m long in a direction 25.0 N of E. Vector B is of unknown length but in a direction of 41.0 E of S. Vector C is also of unknown length but of direction 35.0 N of W. Hiker ends up where he started (A+B+C=0). Find magnitudes of B and C.

Homework Equations

Sine law: (a/sinA)=(b/sinB)=(c/SinC)

The Attempt at a Solution

Ok so i drew the triangle and figured out all of the interior angles:
A=14.0 degrees
B=60.0 degrees
C=106.0 degrees

Also i know side a=1550 m

I used the sin law to get
(a/sinA)=(b/sinB)
(1550/sin14)=(b/sin60)
b=(1550sin60/sin14)
b=5548.6477 m

(a/sinA)=(c/sinC)
(1550/sin14)=(c/sin106)
c=(1550sin106/sin14)
c=6158.829

I was just wondering if I did this right because the numbers look pretty big to me and would like someone to double check for me.

Anyone? Id like to know if there are any errors.

Those numbers are correct.

Thanks a bunch

1. What are displacement vectors?

Displacement vectors are mathematical representations of the distance and direction between two points. They are often used in physics and engineering to calculate the movement of objects.

2. How do you calculate displacement vectors?

To calculate a displacement vector, you must subtract the initial position from the final position. The resulting value will be the magnitude of the vector, and the direction can be determined using trigonometry or other mathematical methods.

3. What is the difference between displacement and distance?

Displacement refers to the straight-line distance and direction between two points, while distance is the total length traveled regardless of direction. Displacement is a vector quantity, while distance is a scalar quantity.

4. How are displacement vectors graphically represented?

Displacement vectors are often represented by arrows on a coordinate plane, with the length of the arrow representing the magnitude of the vector and the direction of the arrow indicating the direction. The starting point of the arrow is the initial position, and the tip of the arrow is the final position.

5. What are some real-world applications of displacement vectors?

Displacement vectors are used in a wide range of fields, including physics, engineering, and navigation. They are used to calculate the movement of objects, such as projectiles, and to determine the displacement and velocity of vehicles and aircraft. They are also used in GPS technology to track the position and movement of objects on Earth.

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