To find out how long it will take for your neighbor to be 9 meters away from your house, we first need to calculate how far your neighbor will move away from you over time due to the sliding of the tectonic plates.
Step 1: Determine the distance change
Currently, you are 10 meters away from your neighbor. You want to know when that distance becomes 9 meters. This means your neighbor needs to move 1 meter closer to you.
Step 2: Find the rate of movement
The plates are sliding past each other at a rate of 5 cm/year, which is equal to 0.05 meters/year.
Step 3: Calculate the time required
To find out how long it will take for your neighbor to move 1 meter closer, we can use the formula: \[ \text{Time} = \frac{\text{Distance}}{\text{Rate of movement}} \] So, \[ \text{Time} = \frac{1 \text{ meter}}{0.05 \text{ meters/year}} = 20 \text{ years} \]
It will take 20 years for your neighbor to be 9 meters away from your house.
Step 4: Calculate the distance after 50 years
Now, to determine how far away you will be from your neighbor after 50 years:
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In 50 years, the plates will cause your neighbor to move: \[ \text{Distance moved} = \text{Rate} \times \text{Time} = 0.05 \text{ m/year} \times 50 \text{ years} = 2.5 \text{ meters} \]
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After 50 years, the new distance between you and your neighbor will be: \[ \text{New distance} = \text{Original distance} + \text{Distance moved} = 10 \text{ meters} + 2.5 \text{ meters} = 12.5 \text{ meters} \]
Summary
- It will take 20 years for your neighbor to be 9 meters away from you.
- After 50 years, you will be 12.5 meters away from your neighbor.