How Do You Calculate Vector Components of Velocity?

[shawonna23]

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.

 

[dextercioby]

Do you know how to use the (circular) trigonometric functions in a rightangle triangle...??

Daniel.

 

[wais]

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.