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

$|r| = \sqrt{16^2 + 8.5^2}$

$|r| = 18 m$

now to find the direction we can use

$tan\theta = \frac{r_y}{r_x}$

$tan\theta = \frac{-8.5}{16}$

$\theta = tan^{-1}(-0.53)$

$\theta = - 28^0$