Relative motion in 1 dimension?

Question

A boat is traveling upstream at 14mph with respect to the river that is flowing at 6mph (with respect to the ground). A man runs directly across the boat, from one side to the other at 6mph (with respect to the boat).
The speed of the man with respect to the ground is:
a 10mph
b 14 mph
c 18.5 mph
d 21 mph
e 26 mph

I have no clue how to work this, my book gives me only problems with parts moving in the same direction. Also, I assume the man is running from side to side and not from the front to the back of the boat? And if he is, I don't think his running is of influence since it's perpendicular to the movementof the boat and river. If he is running from front to back (or back to front) shouldnt the problem state that?
Help : (

Answer 1

...............* --->end of run
.......... *
......... *
........ *
....... *
...... *
..... *
.... *
... *
*---> begin run
man runs across, and boat moves upstream
his speed is horizontal vector (6mph)
and the boat speed is vertical (8mph)
his speedcshould be 10mph

Answer 2

Draw a vector diagram showing river velocity, man's velocity and boat velocity. The man's velocity will be a vector sum. The difference between the river moving in the opposite direction is only the direction (sign) of its vector. Even though he is running side to side, the velocity of the boat and the river are important, as they will add vectorially If you have done problems similar to this with all the velocities in the same direction, this is no different--just the sign of the river velocity is negative. You titled this question motion in one dimension, yet if the man runs side to side (across the boat), this is motion in two directions; maybe that is what is confusing you.

Answer 3

Seems clear to me. You have to assume the boat is moving in the direction it's pointed. The man's running at right angles to the boat's motion. His actual path relative to the ground is the hypotenuse of a right triangle. Use the pythagorean theorem. If I tell you any more I'm doing your homework.