To determine how long it would take for two continents 3000 kilometers apart to collide, given their average speed of movement is 2.5 centimeters per year, follow these steps:
1. Convert the Speed:
The average speed given is 2.5 centimeters per year. To make the calculation easier, we need to convert this speed into kilometers per year.
- There are 100,000 centimeters in a kilometer.
- Therefore, [tex]\( 2.5 \text{ cm/year} \)[/tex] is equivalent to [tex]\( 2.5 \times 0.00001 \text{ km/year} \)[/tex].
- This gives us a speed of [tex]\( 0.000025 \text{ km/year} \)[/tex].
2. Calculate the Time:
To find out how long it will take for the continents to collide, we use the formula for time, which is:
[tex]\[
\text{time} = \frac{\text{distance}}{\text{speed}}
\][/tex]
- The distance between the continents is 3000 kilometers.
- The speed is [tex]\( 0.000025 \text{ km/year} \)[/tex].
- Plugging these values into the formula, we get:
[tex]\[
\text{time} = \frac{3000 \text{ km}}{0.000025 \text{ km/year}}
\][/tex]
- This yields a time of [tex]\( 120,000,000 \text{ years} \)[/tex].
3. Round to One Significant Figure:
To express this time to one significant figure, we round [tex]\( 120,000,000 \text{ years} \)[/tex] to [tex]\( 100,000,000 \text{ years} \)[/tex].
So, it would take approximately [tex]\( 100,000,000 \text{ years} \)[/tex] for the two continents 3000 kilometers apart to collide, when expressed in years to one significant figure.
