Final answer:
To produce a big earthquake with 200 cm of displacement, it would take 40 years at a plate movement rate of 5 cm/year.
Step-by-step explanation:
To compute the number of years of plate motions that must accumulate to produce one big earthquake, one must first know the rate of plate motion and the magnitude of displacement during such an earthquake. According to the question, each big earthquake results in 200 cm (or 2 meters) of displacement along the San Andreas Fault. Given that the plate movement associated with the fault is about 5 cm/year, we can calculate the number of years required to build up enough strain to produce a 2-meter slip.
The calculation is as follows:
Amount of movement per earthquake = 200 cm
Annual plate movement = 5 cm/year
Years needed to accumulate 200 cm = 200 cm รท 5 cm/year
Years needed = 40 years