Question

a car makes a displacement of 100 m towards east and then 200m towards north find the magnitude and direction of the resultant

Answer 1

please see the picture to get your answer

Answer 2

Final Answer : 200√5 m
Direction : tan^(-1) (2) North of East.

Steps and Understanding:
1) We Made the diagram according to given observation.
Then,
In right triangle ABC,
By Pythagoras Theorem,

AC^2 = AB^2 + BC^2
Then, AC =
$= \sqrt{ {100}^{2} + {200}^{2} } \\ = 100 \sqrt{1 + {2}^{2} } \\ = 100 \sqrt{5} m$

3) AC = 100√5 m.

Then, tan(A) = BC/AB = 200/100 = 2
A = tan-1(2)

4) So, Resultant : 100√5m
Direction : tan^(-1)(2) North of East.