Question

If a river originates 200 meters above sea level and travels 400 kilometers to the ocean, what is the average gradient in meters per kilometer?


0.2 m/km


5 m/km


0.5 m/km


2 m/km

Answer 1

To calculate the average gradient of the river, you can use the formula:

\[
\text{Gradient} = \frac{\text{Change in elevation}}{\text{Distance}}
\]

In this case, the change in elevation is from 200 meters above sea level to 0 meters at sea level, which is a change of 200 meters. The distance the river travels is 400 kilometers.

First, we need to convert the distance from kilometers to meters:

\[
400 \text{ km} = 400,000 \text{ meters}
\]

Now, substituting the values into the formula:

\[
\text{Gradient} = \frac{200 \text{ meters}}{400,000 \text{ meters}}
\]

Calculating this gives:

\[
\text{Gradient} = 0.0005 \text{ meters per meter}
\]

To convert this to meters per kilometer, we multiply by 1000:

\[
\text{Gradient} = 0.0005 \text{ m/m} \times 1000 = 0.5 \text{ m/km}
\]

Thus, the average gradient of the river is:

\[
\boxed{0.5 \text{ m/km}}
\]