Question

A girl weighing 407 N hangs suspended on the end of a rope 8 m if a friend pushes her laterally to one side until the rope makes an angle of 35^o with the vertical, what lateral force is required at this point?

Answer 1

Let's write the forces in projections on axis $x$ and $y$:

$$F_{lateral}-Tsin\theta=0,$$ $$Tcos\theta-W_{girl}=0.$$

Let's first find the force of tension in the rope from the second equation:

$$T=\dfrac{W_{girl}}{cos\theta}.$$

Substituting $T$ into the first equation we can find the lateral force:

$$F_{lateral}=W_{girl}tan\theta=407\ N\cdot tan35^{\circ}=285\ N.$$