Question

The x vector component of a displacement vector has a magnitude of 86.2 m and points along the negative x axis. The y vector component has a magnitude of 189 m and points along the negative y axis. Find (a) the magnitude and (b) direction of . Specify the direction as a positive angle with respect to the negative x axis.

Answer 1

Answer:

(a) Magnitude of Vector = 207.73 m

(b) Direction = 65.48°

Explanation:

(a)

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

$Magnitude\ of\ Vector = \sqrt{d_{x}^{2} + d_{y}^{2}} = \sqrt{(86.2\ m)^{2} + (189\ m)^{2}}$

Magnitude of Vector = 207.73 m

(b)

For the direction of the vector we have the formula:

$Direction = tan^{-1}(\frac{y}{x})\\\\Direction = tan^{-1}(\frac{189\ m}{86.2\ m})$

Direction = 65.48°