Imagine a boat is being rowed upstream where v1 is the velocity of the boat and v2 is the velocity of the stream. What is the time required if the boat tends to cross the river along the shortest path?
To find the time required for the boat to cross the river along the shortest path, we can use the concept of relative velocity. The relative velocity of the boat with respect to the stream is the difference between the boat's velocity and the stream's velocity.
Let's assume the speed of the boat is v1 (velocity of the boat) and the speed of the stream is v2 (velocity of the stream).
When the boat is rowing upstream (against the stream), the effective speed of the boat is reduced. The relative velocity can be found by subtracting the stream's velocity from the boat's velocity: v_rel = v1 - v2.
The shortest path across the river will be a straight line, perpendicular to the stream. Therefore, the boat needs to row directly towards the other side of the river.
The distance the boat needs to cross the river is the width of the river, denoted by d.
The time required to cross the river along the shortest path can be calculated using the formula:
time = distance / relative velocity
Therefore, the time required for the boat to cross the river along the shortest path is:
time = d / (v1 - v2)
You can plug in the values of v1, v2, and d into this formula to find the time required.