Question

The horizontal and vertical components of a force are respectively 20 N and 30 N. Calculate the magnitude and direction of the force.

Answer 1

The magnitude of the force can be found using the Pythagoras' Theorem.

Magnitude of the force $= \sqrt{ 20^{2} + 30^{2}} = \sqrt{1300} = 36.05N$

For the direction of the force, $\theta = tan^{-1}(\frac{vertical component}{horizontal component}) = tan^{-1}(\frac{30}{20}$ $)$

$\theta = 56.31^{o}$

Therefore, the magnitude of the force is $36.05 N$ and direction angle of $56.31^{o}$