Question

Find the x and y components of a position vector that has a magnitude of r = 75.0 m and an angle relative to the x-axis of:

(a) 35.0°
(b) 65.0°
a) x-component only
b) y-component only
c) Both x and y components for (a)
d) Both x and y components for (b)

Answer 1

To find the x and y components of a position vector, use trigonometric functions with the given angle and magnitude of the vector.

Step-by-step explanation:

To find the x and y components of a position vector with a magnitude of r = 75.0 m and an angle relative to the x-axis:

(a) To find the x-component only, use the formula: x = r * cos(θ). Substitute the given angle (θ) of 35.0° into the formula to find the x-component.

(b) To find the y-component only, use the formula: y = r * sin(θ). Substitute the given angle (θ) of 65.0° into the formula to find the y-component.

(c) To find both x and y components for (a), follow the steps for finding x-component and y-component.

(d) To find both x and y components for (b), follow the steps for finding x-component and y-component.