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

$|v|=\sqrt{(v_x)^2+(v_y)^2}$

we can plug values

$|v|=\sqrt{(-24.5)^2+(31.5)^2}$

$|v|=39.90614$

Direction:

we can use direction formula

$\theta=tan^{-1}(\frac{v_y}{v_x})$

now, we can plug values

$\theta=tan^{-1}(\frac{31.5}{-24.5})$

$\theta=180-52.12$

$\theta=127.88$................Answer