# Relative Velocity Question

1. Nov 8, 2013

### MathewsMD

A boat is travelling upstream at 14 km/h with respect to a river that is flowing at 6 km/h (with respect to the ground). A man runs directly across the boat, from one side to the other, at 6 km/h (with respect to the boat). The speed of the man to the ground is ____?

Attempt:

vPG = vPB + vBW + vWG
vPG = 6 km/h + 14 km/h - 6 km/h = 14 km/h

That is not the correct answer, though. The answer is 10 km/h. I keep trying different methods but this seems to be the most correct solution...but it's not.

Any help would be greatly appreciated! :)

2. Nov 8, 2013

### Simon Bridge

... which direction is he running compared with the direction the boat is moving?

3. Nov 8, 2013

### TSny

You'll need to treat the velocities as vectors (taking into account that VPB is perpendicular to VBW and VWG).

4. Nov 8, 2013

### MathewsMD

That is the question word for word, and I agree that it is ambiguous.

5. Nov 8, 2013

### MathewsMD

Okay...I treated it as vBW and vPB as parallel since that's what my impression was from reading the question.

I guess that clears up things quite nicely. Thanks.

6. Nov 8, 2013

### Simon Bridge

I don't think it was ambiguous at all - I was trying to direct your attention to the wording.
But you got there in the end.

It can be tricky interpreting word questions. For future reference:

The question says he runs "from one side to the other" ... which would be 90deg to the direction of travel, unless the boat was travelling sideways or something.

The "boat travelling sideways" is the sort of thing the question would make a point of telling you ;)

If he were running parallel to the direction of travel, then he's be going from "front to back" or "from bow to stern" or similar description.