Question

Calculate the magnitude and direction of a vector whose x and y components are given
to be 30 and 40 units respectively.

Answer 1

Answer:

Magnitude = 50 units

Direction = 53.13°

Explanation:

The formula to find out the magnitude of a resultant vector with the help of its x and y components is given as follows:

$Magnitude = \sqrt{x^{2} + y^{2}}$

where,

x = 30 units

y = 40 units

Therefore,

$Magnitude = \sqrt{(30 unit)^{2} + (40\ unit)^{2}}$

Magnitude = 50 units

Now, the direction of the resultant vector will be given by the following formula:

$Direction = tan^{-1}\frac{y}{x}\\\\Direction = tan^{-1}\frac{40}{30}$

Direction = 53.13°