Question

A man moves to go 50 m due south, 40 m due west, and 20 m due north to reach a field. Find what is his displacement from his house to the field?

Answer 1

According to the question, we can draw the path of the man

From the figure, we can write

$CD=BA=40$

In the triangle OCD

We can write,

$OC=\sqrt{{OD}^2+{CD}^2}$

Or, $OC=\sqrt{{30}^2+{40}^2}$

After solving

OC = 50 m

Now for finding direction we can write

$tan\theta =\frac{30}{40}=\frac{3}{4}$

$Or,\theta ={37}^0$

Hence the displacement is 50 m and in the direction 37 degree south of west.