Duty cycle and electronic circuits
Hints (mistake corrected)....

If the duty cycle were 100% the power delivered to the 50 ohm load would be 10^2/50 = 2 watts. Power is proportional to duty cycle of a signal so, if only 1 watt was consumed by the resistor the duty would be 50%.

The above is for average power and not peak power. Peak power, as always would be 2 watts for duty cycles of >0% to 100%.

For the above I'm assuming that the 20Vp-p sinewave is from 0V to +20V and that when the load is connected it will see 0V to +10V as a signal.