Question

A Man has to go 50 M due month, 40 m due east and 20 M due south walk to reach a field.

(a) what distance he has to walk to reach the field?

(b) What is his displacement from his house to the field ?

Answer 1

(a) Distance travelled=50+40+20

=110 m

(b) AF = AB-BF

=AB-DC

=50-20=30 m

His displacement,

$AD=\sqrt{A{F}^2+D{F}^2}$

=$\sqrt{{30}^2+{40}^2}$

= $\sqrt{2500}=50m$

In $\Delta$ AED,

$\tan \theta =\frac{DE}{AE}=\frac{30}{40}=\frac{3}{4}$
$\Rightarrow \theta ={\tan }^{-}1\left(\frac{3}{4}\right)$
His displacement from his house to the field

is 50 m, $ta{n}^{-}1\left(\frac{3}{4}\right)$ north to east.