To determine the age of the wooden cup, you should use Carbon-14 dating. This method is appropriate because Carbon-14 is used for dating organic materials, such as wood, which comes from once-living organisms.
The effective dating range for Carbon-14 is up to about 50,000 years, making it suitable for estimating the age of the wooden cup. On the other hand, Uranium-238 is used for dating geological features and rocks, typically over much longer time scales (millions of years).
Therefore, the correct response is: 1,000-1,040 years; Carbon-14; because wood was once living.