Question

give your answer in component form. (assume that x-axis is horizontal and points to the right, and y-axis points upward.)

Answer 1

To resolve vectors into components, the cosine and sine functions are used. By plugging in the magnitude of the vector and the angle it makes with the x-axis into these functions, the x and y components can be determined. The resultant vector is then expressed in component form and its magnitude can be calculated if needed.

Step-by-step explanation:

To resolve vectors into their components, we use trigonometric identities, specifically the sine function for the y-component and the cosine function for the x-component. For example, if we have a vector A with magnitude 53.0 m at an angle of 20.0° from the x-axis, the components Ax and Ay can be found using the following equations:

• Ax = A cos θ
• Ay = A sin θ

Substituting the given values, we get:

• Ax = 53.0 m × cos(20.0°)
• Ay = 53.0 m × sin(20.0°)

Once the components are calculated, we can express the vector in component form as A = (<Ax>, <Ay>). Similar calculations are done for any other vector, such as vector B with a different magnitude and angle.

Components along the same axis can be added like scalar numbers to find the resultant vector. The resultant's magnitude R can then be calculated using the Pythagorean theorem:

1. R = √(<Rx>² + <Ry>²)