What's their velocity relative to the water?

[Sean1218]

Homework Statement

Boat moving at 2.8 m/s [fwd] relative to water (V_BW)
Tourists walking on deck at 1.1 m/s relative to deck (V_PB)

Determine their velocity relative to the water if they are walking towards the starboard (right side of ship).

Homework Equations

V_PW = V_PB + V_BW

The Attempt at a Solution

V_PW = 1.1 m/s [R] + 2.8 m/s [fwd]

V_PB = 1.1 m/s: x-dir = 0 and y-dir = 1.1 m/s
V_BW = 2.8 m/s: x-dir = 2.8 m/s and y-dir = 0

V_PW = ??: x-dir 2.8 m/s y-dir = 1.1 m/s

So do I just draw a graph? Like, 2.8 in magnitude along the positive x-axis, and then 1.1 in magnitude up (or how would I think about this? like how would I know where to draw the vectors and which direction etc. in a more complicated question?)

and just

c = sqrt(a² + b²)
c = 3.01 m/s
V_PW = 3.01 m/s

Then how do I find the direction of V_PW?

[tan^-1(1.1/2.8)] = [E 21.45 N] or [21.45 N of the horizontal] or what? since the question doesn't use direction

Also, how many significant digits should I leave my answers to (both velocity and direction)?

 

[anathema]

To find the direction of VPW, you can use the inverse tangent function as you did, but it is important to specify the direction in your answer. In this case, the direction would be approximately east of north (E 21.45 N). As for the number of significant digits, it is best to use the same number of significant digits as the given data. In this case, both VBW and VPB have 3 significant digits, so your final answer should also have 3 significant digits (3.01 m/s).