Solving River Flow Velocity: A Motorboat Problem

[abhikesbhat]

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.

 

[tiny-tim]

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!

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.

 

[nlightner]

I would suggest breaking down the problem into smaller, more manageable parts. First, we know that the motorboat overtook the raft at Point A, and then turned back and overtook it again at a distance of 6km from Point A. We also know that the time it took for the motorboat to go from Point A to the turnaround point and back to Point A is 60 minutes.

To solve for the flow velocity, we can use the equation:

Average Speed = Displacement / Time

We know the displacement is 6km (since the motorboat traveled 6km from Point A to the turnaround point) and the time is 60 minutes. However, we need to convert the time to hours, so we can use the equation:

Average Velocity = Displacement / Time

We know the displacement is 6km and the time is 1 hour (since 60 minutes = 1 hour). Therefore, the average velocity of the motorboat is 6km/h.

However, this is only the average velocity. To find the flow velocity, we need to take into account the fact that the motorboat is going both upstream and downstream. Since the duty of the engine is constant, we can assume that the motorboat is traveling at a constant velocity in both directions.

To find the flow velocity, we can use the equation:

Average Velocity = (Velocity upstream + Velocity downstream) / 2

We already know the average velocity is 6km/h, and we can set the velocity upstream and downstream equal to each other since the motorboat is traveling at a constant velocity. Therefore, we can rearrange the equation to solve for the flow velocity:

Flow Velocity = 2 x Average Velocity

Substituting in the value for average velocity, we get:

Flow Velocity = 2 x 6km/h = 12km/h

Therefore, the flow velocity of the river is 12km/h.