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

(a) Magnitude of Vector = 207.73 m

(b) Direction = 65.48°

Step-by-step 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)((y)/(x))\\\\Direction = tan^(-1)((189\ m)/(86.2\ m))\\\\`

Direction = 65.48°