Question:
A motorboat going downstream overcame a raft at a point A; 
= 60 min later it turned back and after some time passed the raft at a distance l= 6.0 km from the point A. Find the flow velocity assuming the duty of the engine to be constant.
Answer:
Two solutions for this problem come to mind. One using the land as frame of reference and second one using raft as the frame of reference. We will discuss both approaches.
A1: Using Land as the frame of reference
Lets call the flow velocity as 
and the motorboat velocity in still water as 
.
Raft velocity = 
(since it goes with the flow of stream)
Thus, Motorboat velocity downstream = 
Motorboat velocity upstream = 
Distance travelled by the motorboad in 
In this time the raft travelled a distance of 
Distance between raft and motor boat = 
This distance is covered by motorboat travelling upstream so the relative velocity is 
So obviously the time taken to cover distance 
at speed 
is 
.
Total time spent is therefore 
.
In this time the raft went a distance of l.
Hence the flow velocity is 
= 3kmph.
A2. Using raft as the frame of reference
Since the raft moves at the flow velocity, the motorboat travels a distance of 
in 
time and then turns around. Upstream its speed is again 
so it takes a total time 
to meet the raft again (by covering 
distance). Total time spent is 
.
In this time, the distance covered by raft is lthe flow velocity is 
= 3kmph.
2 comments:
I understand the first solution, but I have some doubts about the A2. From the reference of the raft the velocity of motorboat should be Vm - Vf.
No. motor boat moves with a speed of Vm w.r.t water. This remains constant regardless of the direction of motor-boats movement.
Post a Comment