Question

A sledge is being pulled by two horses on a flat terrain. The net force on the sledge can be expressed in the Cartesian coordinate system as vector F= (-2980.0i + 8200.0j ) N , where i and j denote directions to the east and north, respectively. Find the magnitude and direction of the pull.

Answer 1

The angle a vector $(a\hat{i}+b\hat{j})$ makes with positive direction of x axis is given by

$\theta = tan^{-1} (\frac{b}{a})$

Here a and b are the components of vector $\vec{F}$ along x and y axis and $\theta$ be the angle made by vector with x axis.

Also the magnitude resultant of a vector of the form $a\hat{i}+b\hat{j}$ is

$|\vec{F}| = \sqrt{a^2+b^2}$

Replacing with our values we have that

$|\vec{F}| = \sqrt{(-2980)^2+(8200)^2}$

$|\vec{F}| = 8724.7N$

Therefore the magnitude of the given force vector is 8724.7N

For the given vector substitute -2980N for a and 8200 N for b in the equation of angle of vector from positive direction of x axis

$\theta = tan^{-1} (\frac{8200}{-2980})$

$\theta = -70.01\°$

Therefore the angle the force vector makes is at -70.01° from east