BOATS AND STREAMS

1.In water ,the direction along the stream is called downstream and ,the direction against the stream is called upstream.

2.If the speed of a boat in still water is u km/hr and the speed of the stream is v km/hr,then:

             speed downstream=(u+v)km/hr.

             speed upstream=(u-v)km/hr.

3.If the speed downstream is a km/hr and the speed upstream is b km/hr,then :

speed in still water=1/2(a+b)km/hr

rate of stream=1/2(a-b)km/hr

PROBLEMS ON TRAINS

1. a km/hr= (a* 5/18) m/s.   

2. a m / s = (a*18/5) km/hr.

3 Time taken by a train of length 1 metres to pass a pole or a standing man or a signal  post is equal to the time taken by the train to cover 1 metres.

4. Time taken by a train of length 1 metres to pass a stationary object of length  b metres is the time taken by the train to cover (1 + b) metres.

5. Suppose two trains or two bodies are moving in the same direction at u m / s and v m/s, where u > v, then their relatives speed = (u - v) m / s.

6. Suppose two trains or two bodies are moving in opposite directions at u m / s and v m/s, then their relative speed is = (u + v) m/s.

7. If two trains of length a metres and b metres are moving in opposite directions at u  m / s and v m/s, then time taken by the trains to cross each other =  (a + b)/(u+v) sec.

8.If two trains of length  a metres and b metres are moving in the same direction

at u m / s and v m / s, then the time taken by the faster  train to cross the slower train = (a+b)/(u-v) sec.

9. If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then

(A's speet) : (B’s speed) = (b^1/2: a^1/2).