1st Question of Kinematics from I.E.Irodov - must for anyone who starts IIT JEE preparation

Q)    A motorboat going downstream overcame a raft at a point A. T= 60 minutes later it turned back and after some time passes a raft at a distance l = 6 km from the point A. Find the flow velocity assuming the duty of the engine to be constant.

Ans.

Let the velocity of the stream = u km/hr

Let the velocity of the motorboat with respect to the stream = v km/hr

Then,

The velocity of the motorboat downstream = v+u km/hr

The velocity of the motorboat upstream = v-u km/hr

The  speed of the raft = speed of the stream = u.

The distance mved by the raft till the motorboat turns back = u(1) km

The distance moved by the motorboat in 1 hour = (u+v )1 km

 The motorboat reaches the turning point in 1 hour. By this time the raft has moved a distance "u" km. Now, the motorboat turns back and moves some distance to meet the raft which is still moving with a speed u.

Time take by the raft to cover the rest of the distance =  (6-u)/u hours.

The distance moved  by the motorboat in this time = (v-u)(6-u)/u km.

So we can say that,

The distance moved by the motorboat to reach the turning point =  Distance between A and the starting point + Distance between the turning point of  the motorboat and the meeting point of the motorboat and the raft. 

Thus,

6 + (v-u)(6-u)/u  =  v+u

This when solved gives us

u = 3 km/hr!!!

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