Question

A car makes a displacement of 200 m towards
east and then 400 m towards north. Find the
magnitude and direction of the resultant.
(A) 2075m, tan-1 (2), N of E
(B) 20/5m, tan-1/2, E of N
(C) 20m, tan-1 (2), N of E
(D) 10m, tan? (2), N of E

Answer 1

Given:

A car makes a displacement of 200 m towards east and then 400 m towards north.

To find:

Magnitude and direction of resultant?

Calculation:

Magnitude of resultant be R :

$R = \sqrt{ {(200)}^{2} + {(400)}^{2} }$

$\implies \: R = \sqrt{ 40000 + 160000 }$

$\implies \: R = \sqrt{200000}$

$\implies \: R = 200 \sqrt{5} \: m$

So, magnitude of resultant is 200√5 metres.

$\tan( \theta) = \dfrac{400}{200} = 2$

$\implies \: \theta = { \tan }^{ - 1} (2) \: N \: of \: E$

So, direction is tan^(-1){2} N of E.

or

$\tan( \phi) = \dfrac{200}{400} = \dfrac{1}{2}$

$\implies \: \phi = { \tan }^{ - 1} (\dfrac{1}{2}) \: E \: of \: N$

So, direction is tan^(-1){½} E of N.