# Vector Problem

1. Sep 15, 2007

### Redstar2

The Problem:

Part 1) A ship cruises forward at $${v}_{s}$$ = 3 m/s relative to the water. On deck, a man walks diagonally toward the bow such that his path forms an angle $$\theta$$ = 22 degrees with a line perpendicular to the boat's direction of motion. He walks at $${v}_{m}$$ = 4 m/s relative to the boat.

At what speed does he walk relative to the water? Answer in units of m/s. Your answer must be within +/- 5%.

Part 2) At what angle to his intended path does the man walk with respect to the water? Answer in units of degrees. Your answer must be within +/- 5%.

Attempt at a solution:

Part 1) What I did was find the velocity in the direction of the boat he was traveling, and I found that to be ~1.5 m/s. And after that, I simply added that to the 3 m/s that the boat was traveling in to find the vector he was traveling at relative to the water to get a vector of 4.5 m/s. However, I'm pretty sure I'm doing this wrong.

Part 2) Wouldn't it just be 0 degrees if I use the 4.5 m/s relative to the water? Again, I'm probably thinking about the entire thing the wrong way.

Any help would be appreciated greatly, thanks guys!

2. Sep 15, 2007

### Staff: Mentor

It's wrong because you ignored the component of his velocity (with respect to the ship) perpendicular to the ship's direction.

With respect to the ship, his path makes an angle of 22 degrees away from the ship's direction of motion. But with respect to the water, what is his direction of motion?

To get the relative velocity of person with respect to the water, you must add the two vectors: A (the boat's velocity with respect to the water) + B (the person's velocity with respect to the boat). Hint: Use components.