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

Magnitude = 50 units

Direction = 53.13°

Step-by-step 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)(y)/(x)\\\\Direction = tan^(-1)(40)/(30)`

Direction = 53.13°