Determine the equation for \$v(t)\$
Given it is a homework question I'm not going to give you a full answer, and you haven't shown any working or attempt, so I'll be even more vague. But you do have enough information to work out what input voltage is. 


You know the real power and power factor of the load, so you can work out the apparent power (real+reactive) into the load.
You also know the voltage across the load (hint: you should know how to find peak from RMS) so knowing the apparent power you can work out the impedance of it.
Once you know the impedance you can work out the current.
Once you know the current you can work out the voltage across the wire impedance.
Once you know the voltage across the wire impedance you can work out the input voltage.