- #1

gnits

- 137

- 46

- Homework Statement
- To find the true winde velocity from the relative wind velocity

- Relevant Equations
- Vr = Va - Vb

Please can I ask for help with the following as to where I'm going wrong.

Book answer is 20 knots and 315 degrees

My solution:

In the below diagram I have sketched the two situations, k is the true speed of the wind.

First question is, is my diagram correct?

The velocity of the wind relaive to the ship ##V_{ws}## is given by:

##V_{ws}=V_w - V_s##

Where ##V_w## is the true velocity of the wind and ##V_s## is the true velocity of the ship.

Let i and j be unit vectors in the directions of east and north respectively

So in the two situations I have:

##k\,sin(22.5)i + k\,cos(22.5)j=V_{w_x}i+V_{w_y}j+20i##

and

##-k\,sin(22.5)i+k\,cos(22.5)j=V_{w_x}i+V_{w_y}j+20j##

Equating coefficients of i and j and solving for ##V_{w_x}## I get:

##V_{w_x}=-10##

and so:

##k=\frac{10}{sin(22.5)}=26.13##

and therefore

##V_{w_y}##=26.13*cos(22.5)=24.13

Which leads to a speed of 26.13 which is not the books answer.

Thanks,

Mitch.

Book answer is 20 knots and 315 degrees

My solution:

In the below diagram I have sketched the two situations, k is the true speed of the wind.

First question is, is my diagram correct?

The velocity of the wind relaive to the ship ##V_{ws}## is given by:

##V_{ws}=V_w - V_s##

Where ##V_w## is the true velocity of the wind and ##V_s## is the true velocity of the ship.

Let i and j be unit vectors in the directions of east and north respectively

So in the two situations I have:

##k\,sin(22.5)i + k\,cos(22.5)j=V_{w_x}i+V_{w_y}j+20i##

and

##-k\,sin(22.5)i+k\,cos(22.5)j=V_{w_x}i+V_{w_y}j+20j##

Equating coefficients of i and j and solving for ##V_{w_x}## I get:

##V_{w_x}=-10##

and so:

##k=\frac{10}{sin(22.5)}=26.13##

and therefore

##V_{w_y}##=26.13*cos(22.5)=24.13

Which leads to a speed of 26.13 which is not the books answer.

Thanks,

Mitch.