Irodov 1.1 Relative Velocity

[razored]

1.1. A motorboat going downstream overcame a raft at point A; T=60 minutes 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.

|------------------------------------------------------------------------------|<< Distance S, the entire length
A ---------------------B(where the two boats meet) ---------------C,( the farthest point the motor boat went)
|------------------------| << this is l which is 6km

B= boat
W=water, or raft
E=earth
When I write B/E i mean boat relative to the earth.
Tau is equal to 60 minutes.
http://mathbin.net/equations/8710_0.png [Broken]

No matter how many times I manipulate the three equations up there, I do not get the answer which is 3 km/hour.

 

[LowlyPion]

Consider it in terms of relative velocity.

When the boat passes the raft, then it is moving off at a relative speed of ... the Velocity of the boat. It goes some distance (60 min * Vb in relative terms) and then turns around.

As it returns it is still going at the same relative velocity isn't it, since they are both still in the same frame of reference of the moving water?

So the return time will be the same as the trip down stream won't it? That makes the total time 2 hours? And from someone looking from the shore they have both ended 6 km down the river?

So ...

 

[razored]

Doesn't the relative speed change because it goes against the current--the speed of the raft--on the way back?

Could you post an additional mathematical equation or revise one? Sorry, I understand things better in equation form sometimes.

 

[LowlyPion]

Doesn't the relative speed change because it goes against the current--the speed of the raft--on the way back?

Could you post an additional mathematical equation or revise one? Sorry, I understand things better in equation form sometimes.

Well in the frame of reference of the river there is no current. If the motorboat moves with constant velocity, then the distance the boat travels from the raft,

d = v*t

The time to travel back then is same d, same v so ... same t.

t + t = 2 t

Distance the river traveled in 2 t is 6 km.

6 km /2 t = 6 km / 2 hr = 3 km/hr.

 

[razored]

Well in the frame of reference of the river there is no current. If the motorboat moves with constant velocity, then the distance the boat travels from the raft,

d = v*t

The time to travel back then is same d, same v so ... same t.

t + t = 2 t

Distance the river traveled in 2 t is 6 km.

6 km /2 t = 6 km / 2 hr = 3 km/hr.

Thank you! I did not realize to figure out the problem you had to think from the perspective of the raft.