# Boats problem

1. Nov 13, 2013

### YummyPotato

I tried looking at the other threads on this but they seem incomplete.
I would like someone to check my work.

1. The problem statement, all variables and given/known data
Two boats are heading away from shore. Boat 1 heads due north at a speed of 3 m/s relative to the shore. Relative to Boat 1, Boat 2 is moving 40° north of east at a speed of 1.7 m/s. A passenger on Boat 2 walks due east across the deck at a speed of 1.1 m/s relative to Boat 2. What is the speed of the passenger to the shore?

2. Relevant equations
x and y vectors.

3. The attempt at a solution
I set up vectors for each moving object.

B1x = 0 B2y = 0

B2x = 1.7cos(40°) B2y = 1.7sin(40°)

Px = 1.1 Py = 0

I added the x and y components

Rx = 0 + 1.302 + 1.1 Ry = 0 + 1.09 + 0

= 2.402 = 1.09

Sp^2 = (2.402)^2 + (1.09)^2
Sp ≈ 4.74 m/s.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Nov 13, 2013

### Mentz114

If those vectors are the velocities relative to the shore, then surely B1x=0 and B1y=3 m/s ? ( y being East).

3. Nov 13, 2013

### haruspex

Don't you mean y being N?

4. Nov 13, 2013

### Mentz114

On re-reading the question, yes, I mean North.