A man floating on a raft in water flowing at 2kmph observes a motor lauch overtaking him at t = 0. Then lauch travels with the speed of 20kmp relative to still water . After travelling for a time of 1 hr , the lauch turns back towards raft.How far from from the original point of crossing do they meet and what is the total time elapsed ?

Explanation

Figure shows point A,B,C and D along bank
A`rarr ` point of crossing for first time.
B,D `rarr` positions of raft and boat when boat turns back .

C `rarr ` Positions of raft and boat during the second crossing
Note : If we fix the observer on the bank, raft has a speed of kph, boat has a speed of `20+2=22`kph for distance AD and `20-2=18 kph` for distance DC.
It is possible to solve w.r.t. bank . However the solution is quite cumbersome.
Fix the observer on raft
W.r.t. raft , the boat has same velocity upstream as well as downstream. Hence, if the boat travels for 1 hr,
while moving away from raft, it travels the same time while approaching the raft,
`:. ` time between two crossings `=t.=2h`. We now find the distance traveled by raft in `2 hr =2xx2=4km`.