## Tuesday, July 10, 2007

### Irodov Problem 1.1

There are two ways of solving this problem, i) from the point of view of an observer on the raft ii) from the point of view of a person on the ground. I will provide both these methods since, I have got a lot of questions on this problem from the readers.

Since the raft is floating on the river, it moves at the same velocity as the river. Let the velocity of the river be s. Let the velocity of the boat in still water be v. This means that the boat's downstream velocity as seen from the ground will be v+s and it upstream velocity as seen from the ground will be v-s.

i) Solution From Reference Frame on the Raft

As seen by an observer on the raft, when the boat moves upstream its velocity will be v (v+s-s)  and it will be -v (-v+s-s) when its moving downstream. Here, positive sign means that the boat is moving away from the raft and negative sign means that the boat is moving towards the raft.

Figure 1 shows the Time-Displacement diagram of the boat and the raft as seen from the point of view of the raft. The slopes of the both upstream and downstream paths of the boat relative to the raft are v and -v.  Let t1 be the time takes by the raft to meet the boat after it turns around. As seen from the figure, it is obvious that

Thus, thus the total time between the two meetings of the raft and the boat is

Now the total distance traveled by the raft is l. This means that,

ii) Solution From Reference Frame on the Ground
The Time-Displacement diagram as seen from the ground of the raft and the boat are shown in Figure 2.

The raft moves at a constant velocity of s downstream (the slope of the line is s) and hence its path is represented by a straight blue line in Figure 2. The boat moves at a speed v+s when  going upstream, represented by a line of slope v+s in Figure 2. The boat turns around and moves at a velocity -v+s when going downstream, represented by a line of negative slope of v-s.

From Figure 2 we can see that,

Now the total distance traveled by the raft is l. This means that,

Krishnanand said...

Thanks for the solution, but still i find the first solution confusing; especially T1=t (1), could you please explain it in detail?

Krishna Kant Chintalapudi said...

Since the raft is moving with the river, as seen from the raft all effects of the river on the boat are absent. So, as seen from the raft, the boat simply moves in still water.

So from from the point of view of the raft, the boat went forward with speed v and then came back with speed v. Hence, t1 = tau.

Hope this clarifies.

Krishnanand said...

Yes, it is clear now ! Thanks

Sahej said...

the best book i have ever practised in my life in the preparation for iit-jee. Guru!chakk de phatte nap de killi!

S.A.M. Mercer said...

thx dude ....
who ever it may be for the solutions

jyoti said...

best book for iit jee preparation..........

Anonymous said...

Thanks a lot dude

ashray said...

shukriya jenab.Tu menu khush kita se.

ANKUR said...

COOOL

ashutosh said...

u r d best :)

Anonymous said...

Thank you sooooo much..... We must solve on our own but still some are difficult to solve. Thanks

Jai said...

hats off to you man.You are a genius.

Anonymous said...

thanks for the solution

Mish Kaushik said...

I know u r trying to help us... But u too know for iit the answer doesnt matters.... Wat matters is the solution, and how we solve it , how much time do we spend on the question, how we develop our brain to get on to the level of iit to crack it. So i think before going through the solutions , students, try the questions . Give them some time, atleast one day . More u practice more u will gain.