Question

A position vector r has the following x and y components. rx = 14.0 m ry = 9.4 m. What is the direction of this vector? Give your answer as an angle measured counterclockwise from the +x direction.

Answer 1

The direction of the position vector r with components rx = 14.0 m and ry = 9.4 m is 34.0° counterclockwise from the +x direction, calculated using the arctangent function.

Step-by-step explanation:

To find the direction of the position vector r given its x and y components, rx = 14.0 m and ry = 9.4 m, we can use the analytical method of vector addition. The direction or angle θ of vector r can be determined using the arctangent function, which is often represented as tan-1 or arctan. Specifically, the formula to find the angle is θ = tan-1(ry/rx), where the angle is measured counterclockwise from the positive x-axis.

Using the given components, we can calculate the direction:

θ = tan-1(9.4 / 14.0)
θ = 34.0° (to the nearest tenth of a degree)

Therefore, the vector r is directed 34.0° counterclockwise from the positive x-axis.

Answer 2

The direction of the vector with components rx = 14.0 m and ry = 9.4 m is approximately 33.7° counterclockwise from the +x direction, calculated using the arctangent of Ry divided by Rx.

Step-by-step explanation:

The direction of a position vector with components rx = 14.0 m and ry = 9.4 m is determined using the analytical method of vector addition.

To find the direction of the vector, we calculate the angle θ with respect to the positive x-axis using the arctangent function:

Step-by-Step Explanation:

Identify the x- and y-components of the vector, which are given as Rx and Ry respectively.

Use the arctangent function to find the angle θ: θ = tan-1(Ry/Rx).

Calculate the angle: θ = tan-1(9.4/14.0) to find the angle in degrees.

Using a calculator, we find that the direction of the vector is approximately 33.7° counterclockwise from the +x direction.