- #1
brotherbobby
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- Homework Statement
- A man swims across a river from
to and back from to , following the line as shown in the figure below. The distance between the two points is . The velocity of the river is and is the same over the entire width of the river, staying constant. As shown in the figure, the line makes an angle with the direction of the river flow and the man swims with a velocity at an angle to the line for both occasions. .
Calculate the time taken by the man for his to and fro journey.
- Relevant Equations
- 1. The relative velocity
of the man with respect to the earth is the vector sum of his velocity with respect to the river and the velocity of the river relative to earth . Thus
2. In order for the man to swim in the given direction (see figure below), it is necessary that the components of his velocity and that of the river to the line cancel out. Thus .
Attempt : It is clear at the outset that, since the velocity of river is constant, the man will not take the same time for the forward and reverse journeys. For both journeys however, the Relevant Equation 2 above will have to hold, since he is constrained to move along
The distance
(2) Backward motion : The motion back to
The distance
Let me put the final answer for the total time with a better look :
This is the answer given in the book, so I am right. However, it ignores the fact that perpendicular to the motion
That equation said
Thus the time of travel is
The angle of the path relative to river flow,
It means therefore that the man will take the same time along any path he chooses provided he keeps the distance
But intuitively, does this make sense? Clearly, the time of travel for the onward journey,
Am I correct in resolving my doubt? A hint would be welcome.