To determine how long it will take for you to be 9 meters away from your neighbor, who is currently 10 meters away, we first need to understand the relative movement due to the transform boundary.
The two plates are sliding past each other at a rate of 5 cm/year (which is 0.05 meters/year). Since you are moving away from your neighbor at this rate, we can calculate the distance between you and your neighbor over time.
Currently, the distance is 10 meters. You want to know when the distance will be 9 meters. The change in distance needed is: \[ 10 , \text{meters} - 9 , \text{meters} = 1 , \text{meter} \]
The rate of separation between you and your neighbor is 0.05 meters per year. We can set up the equation to find the time \( t \): \[ 0.05 , \text{meters/year} \times t = 1 , \text{meter} \] \[ t = \frac{1 , \text{meter}}{0.05 , \text{meters/year}} = 20 , \text{years} \]
So, it will take 20 years for you to be 9 meters away from your neighbor.
Next, to find the distance after 50 years, we can calculate how much further apart you and your neighbor will be after that time: \[ \text{Distance change} = 0.05 , \text{meters/year} \times 50 , \text{years} = 2.5 , \text{meters} \] Now, add this distance change to the current distance: \[ \text{New distance} = 10 , \text{meters} + 2.5 , \text{meters} = 12.5 , \text{meters} \]
Therefore, after 50 years, the distance from you to your neighbor will be 12.5 meters.