P$\mathrm{.}9-15$ A generator with an open$-$circuit voltage $v_{}(t)=10sin8000t(V)$ and internal impedance $Z_{}=40+j30()$ is connected to a $50()$ distortionless line. The line has a resistance of $0\mathrm{.}5(\frac{}{m}),$ and its lossy dielectric medium has a loss tangent of $0\mathrm{.}18\%.$ The line is $50(m)$ long and is terminated in a matched load. Find $($a$)$ the instantaneous expressions for the voltage and current at an arbitrary location on the line, $($b$)$ the instantaneous expressions for the voltage and current at the load, and $($c$)$ the average power transmitted to the load.