Final answer:
The average velocity of the water in the mountain stream is calculated to be 5,000 m/s, which is unreasonable and suggests an inconsistency in the given flow rate or an error in the problem's premises.
Step-by-step explanation:
Average Velocity in a Mountain Stream
To calculate the average velocity of water flowing through a stream, we can use the equation for volume flow rate, which is defined as the product of the cross-sectional area (A) of the stream and the average velocity (V) of the water. The equation is represented as:
Flow rate (Q) = A * V
For the mountain stream with a width of 10.0 m and an average depth of 2.00 m, we can find the cross-sectional area by multiplying the width by the depth, resulting in:
A = 10.0 m * 2.00 m = 20.0 m²
Using the given flow rate (Q) of 100,000 m³/s, we can rearrange the flow rate equation to solve for the average velocity (V):
V = Q / A
V = 100,000 m³/s / 20.0 m² = 5,000 m/s
However, this calculated average velocity is unreasonable. It's significantly higher than the velocity of water coming out of a hose with no nozzle, which is about 1.96 m/s. The discrepancy indicates that there could be an error in the given values or an inconsistency in the premises.