# Constant velocity and turning around

1. Sep 19, 2013

### fogvajarash

1. The problem statement, all variables and given/known data
A vacationer gets into his out-board motorboat and leaves a dock on a river bank for a day of fishing. Just as he turns upstream, he hears a splash but pays no attention and continues cruising at normal speed. 30.0 minutes later he realizes that his watertight lunchbox is missing. He then turns downstream, with the motor still set at cruising speed. He sights his lunchbox floating down the river and retrieves it at a point 0.2 km downstream of the dock. How long after turning around does he pick up his lunch?

2. Relevant equations
v = s/t

3. The attempt at a solution
I can't figure out anything in the problem. I don't know how to set it up.

2. Sep 19, 2013

### phinds

Draw vectors.

3. Sep 19, 2013

### johnqwertyful

"Constant velocity and turning around"

Just a tip, you can't have constant velocity and turn around. With velocity, direction matters. What you mean is speed.

4. Sep 19, 2013

### fogvajarash

Okay

5. Sep 19, 2013

### fogvajarash

Draw the vectors for the velocity? The only one remaining then would be the one that is down the stream by 0.2km. How can i proceed from that?

Thank you very much

6. Sep 19, 2013

### phinds

When I said "draw the vectors" what I meant was DRAW THE VECTORS! Show us your work so we can see exactly where you are stuck.

7. Sep 19, 2013

### Staff: Mentor

An important question to ask oneself when presented with this sort of question is, what are the given velocities measured with respect to? In this case, how is one to define the "cruising speed" of the boat? Does the answer to that question make things easier or harder?

8. Sep 22, 2013

### fogvajarash

Isn't the "cruising speed" of the boat sort of the boat sailing at constant velocity (in the points in which the boat isn't changing direction)? I'm really lost in this problem.

9. Sep 22, 2013

### phinds

Draw the vectors

10. Sep 22, 2013

### Staff: Mentor

"Cruising speed" is generally taken to mean a set speed that the boat runs at for long periods of time, particularly when no maneuvering is required. Typically it would correspond to a particular setting of the throttle on the motor.

The question to ask yourself is, what is this velocity measured with respect to?

11. Sep 22, 2013

### fogvajarash

Isn't this velocity measured with respect to where the boat departs from (say the dock?)

12. Sep 22, 2013

### fogvajarash

I've got the vectors in here

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13. Sep 22, 2013

### Staff: Mentor

Nope. The setting of the throttle on the motor has no connection to the dock. The boat has no idea if its running up-stream, down-stream, or any direction related to the shore. The only thing the boat is mechanically "connected" to is the water itself...

14. Sep 22, 2013

### fogvajarash

Okay. How can I proceed from knowing that fact?

15. Sep 22, 2013

### Staff: Mentor

Well, that's the sneaky bit that gives away the solution to these types of problems

If the boat's speed is always relative to the water it travels through, then for events that occur only on the water you can take the water itself as the frame of reference (where you base your coordinate system).

Forget the dock, forget the banks, forget the land entirely. For all intents and purposes you are moving on a motionless surface that is the body of water (in your mind, transform the river to a motionless lake). Now reinterpret the problem from the moment that the lunch box is dropped.

16. Sep 22, 2013

### fogvajarash

Thank you so much gneill!! I finally got the answer which is 30.0min.

17. Sep 22, 2013

### Staff: Mentor

I told you it was sneaky.