To calculate the distance between you and your neighbor after 50 years, first, we need to determine how much the plates will move in that time.
The plates are sliding past each other at a rate of 5 cm per year. Over 50 years, the total movement will be:
\[ 5 \text{ cm/year} \times 50 \text{ years} = 250 \text{ cm} \]
Since 1 meter equals 100 cm, we can convert 250 cm to meters:
\[ 250 \text{ cm} = 2.5 \text{ m} \]
Initially, you are 10 meters away from your neighbor. As the plates move, this distance will increase by 2.5 meters. Therefore, the new distance will be:
\[ 10 \text{ m} + 2.5 \text{ m} = 12.5 \text{ m} \]
After 50 years, the distance between you and your neighbor will be 12.5 meters.