Answer
They can lift it about 2.51m above the ground.
Work Step by Step
First, we will use the ultimate tensile strength of nylon to find the force at which it breaks. Therefore;
$F=500*10^6N/m^2*A$
$F=500*10^6N/m^2*\pi (.5*0.00115m)^2$
$F=519.3N$
Now, we can sum the forces vertically and then set the tension in the cord to 519.3N to find the angle of the wire. Therefore;
$(\uparrow +) \sum \overrightarrow{F}_{y} =0 $
$2T\sin\theta-25.0kg*9.8m/s^2=0$
$\sin\theta=\frac{25.0kg*9.8m/s^2}{2T}$
$\theta=\arcsin\frac{25.0kg*9.8m/s^2}{2T}$
$\theta=\arcsin\frac{25.0kg*9.8m/s^2}{2*519.3N}$
$\theta\approx13.64^{\circ}$
Now we can find the amount the wire sags, x.
$\tan13.64^{\circ}=x/2m$
$x=2m*\tan13.64^{\circ}$
$x\approx0.485m$
We know the pole is 3m tall, so now we can find the height above the ground.
$3m-0.485m=2.51m$
They can lift it about 2.51m above the ground.
