The Story of The Indecisive Rower

A rower rows regularly on a river, from A to B and back. He’s got into the habit of rowing harder when going upstream, so that he goes twice as fast relative to the water as when rowing downstream. 

One day as he’s rowing upstream he passes a floating bottle. He ignores it at first but then gradually grows curious about its contents. After 20 minutes of arguing with himself he stops rowing and drifts for 15 minutes. Then he sets out after the bottle. After some time rowing downstream he changes his mind, turns around, and makes his way upstream again. But his curiosity takes hold once more, and after 10 minutes of rowing upstream he turns and goes after the bottle again. Again he grows ashamed of his childishness and turns around. But after rowing upstream for 5 minutes he can’t stand it any longer, rows downstream, and picks up the bottle 1 kilometer from the point where he’d passed it. 

How fast is the current?

That's the speed of water current!

Water Speed in The Story of The Indecisice Rower

What was the story?

Just for a moment let's assume the rower is rowing on a calm lake where water is stationary. Then, the bottle that he saw is also not moving & floating at one point.

In the case, he moves away (upstream in real case) from the bottle & comes back (downstream in real case) again to collect the bottle. He rows away from the bottle for 20 + 10 + 5 = 35 minutes. 

Remember his speed is double when he goes away from bottle than when he is coming towards the bottle. That's why he takes 35 X 2 = 70 minutes to come back at the point where bottle is floating.

Moreover, he drifts for 15 minutes in real case; for that let's assume he sits motionless for 15 minutes (in our assumed lake case) at some point in between.

So after leaving the bottle, he returns to the bottle after 35 + 15 + 70 = 120 minutes.

Now, assume this water in the lake is moving and this bottle is 'displaced' by 1 KM away from it's original position in 120 minutes. 

That means, the water is moving at the speed of 1 km / 120 minutes. That is the speed of water current is 1/2 kmph.  

How it Will Affect the Water Level?

A man stuck in a small sailboat on a perfectly calm lake throws a stone overboard. It sinks to the bottom of the lake.

When the water again settles to a perfect calm, is the water level in the lake higher, lower, or in the same place compared to where it was before the stone was cast in?

Did you think it will rise? 

Physics : Finding the Effect on the Water Level

But why water level was affected?

Do you recall what does Archimedes Principle state? For an object to float on water, it has to displace that much volume of water whose weight is equal to weight of the object itself. Now if object has less density than water then obviously it has to displace lesser amount of volume of water to float on it. That means it has to sink less in water.

For a moment, let's assume the stone has very high density & hence having weight equal to hundreds of kilograms despite of having small volume.

Here, stone sinks to the bottom of the lake suggests that it is has more density than water. It can't displace the water whose weight is equal to it's weight.But when it was on sailboat it could push the sailboat down so that more water is displaced weighing equal to it's weight. Result of this, the sailboat sinks little 'deeper' compared to when stone wasn't there.

Obviously, the volume of displaced water when stone was in sailboat (due to stone only) must be greater that the volume of displaced water when stone sinks to the bottom of the lake. That's why both sailboat and stone together could float on the water. In short, sailboat helped stone to displace amount of water needed to float which results in rise in shoreline.

And when stone is thrown out of the sailboat, then ideally it can't displace more water than when it was on sailboat. Now, sailboat sinks less 'deeper' in water displacing only water need to float itself. 

That's why the water level must be dropped compared to earlier. The little rise due to water displaced by stone can't exceed the earlier water level for the reason explained above.