Question

IP The x and y components of a vector r⃗ are rx = 16 m and ry = -8.5 m , respectively

Find the direction and of the vector r⃗.
Express your answer using two significant figures.

Answer 1

as it is given that

`r_x = 16 m`

`r_y = -8.5 m`

now we will have

`\vec r = 16 \hat i - 8.5 \hat j`

now the magnitude of this vector is given as

`|r| = √(16^2 + 8.5^2)`

`|r| = 18 m`

now to find the direction we can use

`tan\theta = (r_y)/(r_x)`

`tan\theta = (-8.5)/(16)`

`\theta = tan^(-1)(-0.53)`

`\theta = - 28^0`