Rope Tension Vector Problem

[nerd]

This is the problem and my work. I dont know where to go next. Please help!

 

[Deleted member 4993]

This is the problem and my work. I dont know where to go next. Please help!View attachment 31129View attachment 31130

First,
edited
Define 'x' and 'y' (orthogonal) directions according to your convenience.

Cut the rope and replace it with a tension T (directed along the rope)

Draw the FREE BODY DIAGRAM of the tether ball (assumed to be a particle, with tension in the rope (T), weight W (= 1 lb) & the pulling force (u).

Now apply conditions of equilibrium. $\displaystyle \sum F_x = 0$ .... and .... $\displaystyle \sum F_y = 0$

Continue .....

 

[nerd]

This is my work so far. I reached a dead-end, though. Am I doing anything wrong?

 

[BigBeachBanana]

Right triangles are your friends.
To find the resulting tension $|\overrightarrow{t}|$:
$$\cos(\theta)=\frac{|\overrightarrow{w}|}{|\overrightarrow{t}|}$$To find the magnitude of $|\overrightarrow{u}|$:
$$\tan(\theta)=\frac{|\overrightarrow{u}|}{|\overrightarrow{w}|}$$

 

[nerd]

Got it! Thanks a lot!