Question

a vector has a x component of -25 units and y component of 40 units find the magnitude and direction

Answer 1

Answer:

47.2 units at $122^{\circ}$

Explanation:

The components of the vector are:

x = -25

y = 40

The two components form the sides of a right triangle, of which the vector itself represents the hypothenuse; therefore, we can find the magnitude of the vector by using the Pythagorean theorem:

$v=\sqrt{x^2+y^2}=\sqrt{(-25)^2+(40)^2}=47.2$

Concerning the direction, we can apply the formula:

$\theta =tan^{-1} (\frac{y}{|x|}) = tan^{-1}(\frac{40}{25})=58.0^{\circ}$

The x-component is, however, negative, so the correct angle (measured anticlockwise from the positive x-axis) is

$\theta = 180 -58 = 122^{\circ}$