A rower whose speed of rowing is u crosses a river of width s to a point exactly opposite. Find the time of the journey if the speed of the stream is V( less than u)
at time t, we must have
s^2 + (vt)^2 = (ut)^2
(u^2 - v^2)t^2 = s^2
t = s/√(u^2-v^2)
To find the time of the journey, we need to calculate the effective speed of the rower while crossing the river, taking into account the stream's speed.
Let's break down the situation:
1. The rower's speed of rowing is u.
2. The width of the river is s.
3. The speed of the steam is V, which is less than u.
When crossing the river, the rower needs to account for the force of the stream pushing them downstream. This means they must row diagonally, aiming upstream to counteract the effect of the stream.
To calculate the effective speed of the rower, we can use the Pythagorean theorem. Let's denote the effective speed as veff.
veff = √(u^2 - V^2)
The time it takes for the rower to cross the river is given by:
time = distance / veff
In this case, the distance is the width of the river, s.
time = s / √(u^2 - V^2)
Thus, the time of the journey is s divided by the square root of the difference between the rower's speed squared and the stream's speed squared.