Solving River Flow Velocity: A Motorboat Problem

AI Thread Summary
The problem involves a motorboat traveling downstream and later turning back to pass a raft 6 km from the starting point after 60 minutes. The raft moves at the speed of the river, while the boat maintains a constant speed relative to the water. To solve for the flow velocity, one must establish equations based on the boat's speed (v) and the time taken for the return journey (T). The discussion emphasizes the importance of understanding the relationship between the boat's speed, the river's flow, and the distances involved. A clear approach involves setting up equations to express these variables effectively.
abhikesbhat
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Homework Statement



A motorboat is going downstream overcame a raft at a Point A; t=60 min later it turned back and after some time passed the raft at a distance l=6km from point A. Find the flow velocity assuming the duty of the engine to be constant.

Homework Equations



Average Speed,Displacement, Average Velocity

The Attempt at a Solution


I drew a picture and got confused. I think I don't understand the question.
 
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abhikesbhat said:
A motorboat is going downstream overcame a raft at a Point A; t=60 min later it turned back and after some time passed the raft at a distance l=6km from point A. Find the flow velocity assuming the duty of the engine to be constant.

Hi abhikesbhat! :smile:

The raft is moving at the same speed as the river.

The boat is moving at a fixed speed relative to the river.

Call that fixed speed v, and the time for the second part of the boat's journey T, and write a couple of equations for v and T. :smile:
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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