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Question
Land west of the San Andreas fault in southern California is moving at an average velocity of about 6 cm/y northwest relative to land east of the fault. Los Angeles is west of the fault and may thus someday be at the same latitude as San Francisco, which is east of the fault. How far in the future will this occur if the displacement to be made is 590 km northwest, assuming the motion remains constant?
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Final Answer
10 million years
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OpenStax College Physics Solution, Chapter 2, Problem 8 (Problems & Exercises) (1:40)

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Video Transcript

This is College Physics Answers with Shaun Dychko. Los Angeles is on one side of the San Andreas fault and San Francisco is on the other side so parts west of the fault line are moving to the north-west— here are the directions here, this is north-west like that— and it's moving at 6 centimeters every year and the question is at some point, Los Angeles will be at the same latitude as San Francisco and how long will it take to get there? Well the average velocity of Los Angeles is its displacement divided by time and we can solve this for time. So we'll multiply both sides by <i>t</i> and divide both sides by <i>v</i> bar and the <i>v</i> bars cancel on the left and the <i>t</i>'s cancel on the right leaving us with time is displacement divided by average velocity, I guess that deserves a bar on the top right there, okay. So that's 590 kilometers is the total displacement to cover and divided by the speed which is 6 centimeters per year and this centimeters needs to be converted into kilometers in order to cancel with the kilometers that are in the numerator and the units of our answer will be years because we have years in the denominator of the denominator. Okay. So we have about 10 milllion years to wait before Los Angeles gets to the same latitude as San Francisco.