Question

Two ropes apply a force to a boat. The first is 700 N in the positive x direction and 300 N in the positive y direction. In At what angle (clockwise from the positive x-axis) must a third rope tension be applied in order to keep the boat at rest?

Answer 1

Answer:

$\theta=156.81^{\circ}$

Explanation:

It is given that,

Force due to rope 1, $F_x=700\ N$

Force due to rope 2, $F_y=300\ N$

Let $\theta$ is the angle must a third rope tension be applied in order to keep the boat at rest. It can be given by :

$tan\theta=\dfrac{F_y}{F_x}$

$tan\theta=\dfrac{300}{700}$

$\theta=23.19^{\circ}$

The angle clockwise from the positive x-axis will be equal to,

$\theta=180-23.19$

$\theta=156.81^{\circ}$

So, the angle must a third rope tension be applied in order to keep the boat at rest is 156.81 degrees. Hence, this is the required solution.