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

A man floating on a raft in water flowing at 2 kmph observes a motor l

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