Question

vector B is 55.1 m units long in a 13.9 degree direction. What is the X and y component of this vector?

Answer 1

To find the x and y components of vector B, we can use trigonometry. The x component represents the horizontal displacement, while the y component represents the vertical displacement.

First, let's find the x component. We can use the formula:

x = length of vector B * cos(angle)

Substituting the values given in the question:

x = 55.1 m * cos(13.9 degrees)

Using a calculator, we find:

x ≈ 53.92 m

Therefore, the x component of vector B is approximately 53.92 m.

Next, let's find the y component. We can use the formula:

y = length of vector B * sin(angle)

Substituting the values given in the question:

y = 55.1 m * sin(13.9 degrees)

Using a calculator, we find:

y ≈ 12.49 m

Therefore, the y component of vector B is approximately 12.49 m.

To summarize:

The x component of vector B is approximately 53.92 m, and the y component is approximately 12.49 m.

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Answer 2

Answer: Therefore, the X component of the vector B is 52.8 m and the Y component is 13.5 m.

Explanation: To find the X and Y components of a vector given its magnitude and direction, we use the following formulas:

X = magnitude * cos(direction)

Y = magnitude * sin(direction)

Using these formulas with the given values, we get:

X = 55.1 * cos(13.9) = 52.8 m

Y = 55.1 * sin(13.9) = 13.5 m

Therefore, the X component of the vector B is 52.8 m and the Y component is 13.5 m.