Question

The components of vector are ax and ay (both positive), and the angle that it makes with respect to the positive x axis is θ. Find the angle θ if the components of the displacement vector are (a) ax = 12 m and ay = 12 m, (b) ax = 20 m and ay = 12 m, and (c) ax = 12 m and ay = 20 m.

Answer 1

we can use formula

`\theta=tan^(-1)((a_y)/(a_x))`

(a)

we are given

`a_x=12,a_y=12`

now, we can plug values

`\theta=tan^(-1)((12)/(12))`

`\theta=tan^(-1)(1)`

`\theta=(\pi)/(4)rad`

(b)

we are given

`a_x=20,a_y=12`

now, we can plug values

`\theta=tan^(-1)((12)/(20))`

`\theta=tan^(-1)((3)/(5))`

`\theta=30.96^(\circ \:)`

(c)

we are given

`a_x=12,a_y=20`

now, we can plug values

`\theta=tan^(-1)((20)/(12))`

`\theta=tan^(-1)((5)/(3))`

`\theta=59.03^(\circ \:)`