Two Boats in a stream – part 2

Hope you found the two questions of the lasts post pretty easy to solve. And believe me, when I say, most uninitiated students would have found the questions tough. Here goes the thought process of solving them …

Q. 5: From the instance the boat crosses the wooden piece to the instant the boat meets the wooden piece again, on its way back, time elapsed is 1 + 1 i.e. 2 hours. And in these two hours, the wooden piece has travelled 8 km, because of the stream. Thus, speed of the stream = 4 km/hr.

Q. 6: This question is also exactly similar to the earlier question. The only difference being that in this question the time taken, after turning back, to meet the hat again is not given.
Well the entire purpose of the last post was just to drive in this point. The boat and the hat are drifting apart for 10 minutes and then, the boat turns back. The boat will again take 10 minutes to reach back to the hat.

Thus, in a total of 20 minutes, the hat travels a 100 mts due to the stream and hence speed of the stream is 5 m/min i.e. 1/12 m/s

If you are still struggling to accept the fact that the boat takes, the same time, 10 mins to reach back to the hat, you have to go back to the earlier post and convince yourself about the simplicity of the idea that when two objects are in the same stream, the presence of stream just does not play any role in the relative speeds.
This is to say, that even in Q. 5 the time taken by the boat from port to reach back to the wooden piece was redundant, it had to be 1 hour and nothing else.

For those who are yet arguing that while the boat was moving away from the hat, the boat is only inching slowly away from the hat because both are in the same direction, whereas when the boat is moving towards the hat, it is reaching the hat faster because they are in opposite direction – this is false reasoning. The relative speed in both the cases is exactly the same, relative speed being the speed of the boat. Use variables to convince yourself. When the boat is moving towards the hat, the stream is hindering the boat.

Position of meeting

Another question raised in the last post was that the stream would surely have some effect, but what would that be? The effect would be the position of the meeting point, with reference to an observer, standing on the shore.

In each of Q. 2, 3 and 4, since the boats are travelling apart for 4 hours, they would take further 4 hours to meet after turning back. Since the time taken to move apart and the time taken to close-in the gap is the same, does this mean that they meet at the same point as where they started from?

This would have been the case if they were on land. Say they start from point A, then they would meet again at the same point A.

And if they are in a stream, the stream has an effect here. The effect is that point A is on a stream and hence the point is floating point i.e. from an observer’s point of view, this point will move along the stream.

In Q. 2 & 3, this point, being on a stream, would have moved downstream in the 8 hours that they took to meet, since starting to row apart. Thus, the meeting point would be downstream from the starting point at a distance equal to the distance that the stream travels in 8 hours.

And in Q. 4, this point A would have travelled downstream for 4 hours and then since the stream changes its direction would have moved 4 hours in the other direction i.e. would reach back to exactly the same point from where the boats started (from an observer’s point of view). Thus, in this question, the meeting point would have been the same as where the two boats started from.

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