How Do You Calculate Vector Components of Velocity?

In summary, the components of a vector are the two or three quantities that describe its magnitude and direction. They can be calculated using trigonometric functions, and can be negative to indicate the direction of the vector. The components directly affect the magnitude of the vector, which can be represented graphically using a vector diagram.
  • #1
shawonna23
146
0
The speed of an object and the direction in which it moves constitute a vector quantity known as the velocity. An ostrich is running at a speed of 17.0m/s in a direction of 68.0 degrees north of west. What is the magnitude of the ostrich's velocity component that is directed at A. due north and B. due west?

I think I have drawn the right picture for this problem, but I'm lost on how to write the components down.
 
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  • #2
Do you know how to use the (circular) trigonometric functions in a rightangle triangle...??

Daniel.
 
  • #3


You are correct in drawing a picture to visualize the problem. In this case, the velocity of the ostrich can be represented by a vector with a magnitude of 17.0 m/s and a direction of 68.0 degrees north of west.

To find the components of this vector, we can use basic trigonometry. The component directed due north would be the adjacent side of the right triangle formed by the velocity vector and the due west direction. Similarly, the component directed due west would be the opposite side of the triangle.

To find the magnitude of the component directed due north, we can use the cosine function:

cos(68.0 degrees) = adjacent/hypotenuse

Adjacent = cos(68.0 degrees) * 17.0 m/s = 6.94 m/s

Therefore, the magnitude of the ostrich's velocity component directed due north is 6.94 m/s.

To find the magnitude of the component directed due west, we can use the sine function:

sin(68.0 degrees) = opposite/hypotenuse

Opposite = sin(68.0 degrees) * 17.0 m/s = 15.83 m/s

Therefore, the magnitude of the ostrich's velocity component directed due west is 15.83 m/s.

In summary, the components of the ostrich's velocity are 6.94 m/s directed due north and 15.83 m/s directed due west. These components make up the overall velocity vector of 17.0 m/s at 68.0 degrees north of west.
 

FAQ: How Do You Calculate Vector Components of Velocity?

1. What are the components of a vector?

The components of a vector are the two or three quantities that describe its magnitude and direction. These are typically represented by the x and y coordinates in a two-dimensional vector, and the x, y, and z coordinates in a three-dimensional vector.

2. How are the components of a vector calculated?

The components of a vector can be calculated using trigonometric functions. The x component is equal to the magnitude of the vector multiplied by the cosine of the angle between the vector and the x-axis. The y component is equal to the magnitude of the vector multiplied by the sine of the angle between the vector and the y-axis. In a three-dimensional vector, the z component is calculated in a similar manner using the cosine and sine of the angle between the vector and the z-axis.

3. Can the components of a vector be negative?

Yes, the components of a vector can be negative. This indicates that the vector is pointing in the opposite direction of the positive axis. For example, a vector with a negative x component would be pointing towards the left on a two-dimensional coordinate system.

4. How do the components of a vector affect its magnitude?

The components of a vector directly affect its magnitude. The magnitude of a vector is calculated using the Pythagorean theorem, which states that the square of the vector's magnitude is equal to the sum of the squares of its components. In other words, the larger the components of a vector, the larger its magnitude will be.

5. Can the components of a vector be represented graphically?

Yes, the components of a vector can be represented graphically using a vector diagram. In a two-dimensional vector, the x and y components can be represented by drawing arrows along the x and y axes, respectively. The vector itself can be represented by the diagonal line connecting the tips of the arrows. In a three-dimensional vector, the x, y, and z components can be represented by drawing arrows along the x, y, and z axes, respectively, and the vector is represented by the diagonal line connecting the tips of the arrows.

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