How Is the Speed of a Man Calculated When Running Across a Boat Moving Upstream?

[MathewsMD]

A boat is traveling 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:

v_PG = v_PB + v_BW + v_WG
v_PG = 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! :)

 

[Simon Bridge]

A man runs directly across the boat, from one side to the other, at 6 km/h

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

 

[TSny]

You'll need to treat the velocities as vectors (taking into account that V_PB is perpendicular to V_BW and V_WG).

 

[MathewsMD]

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

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

 

[MathewsMD]

You'll need to treat the velocities as vectors (taking into account that V_PB is perpendicular to V_BW and V_WG).

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

I guess that clears up things quite nicely. Thanks.

 

[Simon Bridge]

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

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 traveling sideways or something.

The "boat traveling 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.