To solve this problem, we need to understand how the movement of the tectonic plates will affect the distance between you and your neighbor over time.
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How long will it take to be 9m away from your neighbor?
You start with a distance of 10 meters from your neighbor. To be 9 meters away, the distance between you and your neighbor must decrease by 1 meter.
The plates are sliding past each other at a rate of 5 cm/year, which is equivalent to 0.05 meters per year. Since the distance needs to decrease by 1 meter, we can calculate the time it will take:
\[ \text{Time} = \frac{\text{Distance to decrease}}{\text{Rate of movement}} = \frac{1 \text{ m}}{0.05 \text{ m/year}} = 20 \text{ years} \]
So, it will take 20 years to be 9 meters away from your neighbor.
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What will be the distance after 50 years?
In 50 years, the plates will have moved apart by:
\[ \text{Distance moved} = \text{Rate of movement} \times \text{Time} = 0.05 \text{ m/year} \times 50 \text{ years} = 2.5 \text{ m} \]
Since we want to find the new distance between you and your neighbor after this movement, we add the distance moved to the initial distance:
\[ \text{New distance} = \text{Initial distance} + \text{Distance moved} = 10 \text{ m} + 2.5 \text{ m} = 12.5 \text{ m} \]
After 50 years, the distance between you and your neighbor will be 12.5 meters.