Question

A vector has an x-component of −24.5 units and a y-component of 31.5 units. Find the magnitude and direction of the vector.

Answer 1

we are given a vector

whose

x-component is -24.5

so,
`v_x=-24.5`

y-component is 31.5

so,
`v_y=31.5`

Magnitude:

we can use formula

`|v|=√((v_x)^2+(v_y)^2)`

we can plug values

`|v|=√((-24.5)^2+(31.5)^2)`

`|v|=39.90614`

Direction:

we can use direction formula

`\theta=tan^(-1)((v_y)/(v_x))`

now, we can plug values

`\theta=tan^(-1)((31.5)/(-24.5))`

`\theta=180-52.12`

`\theta=127.88`................Answer