91Ó°ÊÓ

A river current is the natural water flow in a river. It can significantly affect the movement of objects like boats. In this problem, the river has a consistent current speed of 5 meters per second. This velocity impacts the boat's speed during both upstream and downstream travel.
When navigating upstream, the river current works against the boat. But when traveling downstream, it aids the boat's movement. Knowing the speed of the river current is key for solving problems related to motion in a river environment. It allows us to adjust the boat's speed calculations accordingly. This adjustment is crucial for determining the effective speed of travel in each direction.

Relative velocity involves calculating how fast an object appears to move from different viewpoints. It's useful in situations where there are multiple motions influencing an object's overall speed. For the boat traveling in a river, the relative velocity depends on both its speed in still water and the flow of the river current.
To find the boat's actual speed relative to the riverbank:

• Upstream, subtract the river's speed from the boat's still-water speed.
• Downstream, add the river's speed to the boat's still-water speed.

In this exercise, the relative velocity upstream is determined by subtracting 5 m/s (the current's speed) from 7.5 m/s (the boat's speed). Downstream, the relative velocity is the sum of these speeds. Using relative velocity helps us calculate the time taken for travel in different conditions.

When dealing with river travel, understanding upstream and downstream motion is essential. These terms describe how the movement is affected by the river current.
Upstream motion is against the flow of the river, leading to reduced effective speed. The current slows the boat down, making the journey longer. In this problem, the upstream speed is the boat's speed minus the current speed, resulting in 2.5 m/s.
Downstream motion is with the flow of the river, increasing the effective speed. This cooperation means the boat moves faster. Here, downstream speed is the boat's speed plus the current speed, resulting in 12.5 m/s. Knowing both speeds enables accurate calculation of travel time for each part of the trip.

To compute the time needed for the boat's journey, we apply the basic physics formula: \[ \text{time} = \frac{\text{distance}}{\text{speed}} \]This formula requires knowing the distance of travel and the effective speed for each leg of the journey. For this 500-meter upstream and downstream trip, having the right speed values is crucial.
Using the determined effective speeds:

• Upstream takes 200 seconds (\[ \frac{500 \text{ m}}{2.5 \text{ m/s}} \]).


• Downstream takes 40 seconds (\[ \frac{500 \text{ m}}{12.5 \text{ m/s}} \]).

The total round trip time is the sum of these times, which is 240 seconds. Calculating time this way highlights how different conditions affect travel duration.