- #1

gnits

- 137

- 46

- Homework Statement
- To find the relative velocity of the wind as seen from a car

- Relevant Equations
- Vab=Va-Vb

Could I please ask for any help with the following question:

Here's my attempt: (i and j are unit vectors in the directions of east and north respectively)

(apologies that LaTeX is simply not working for me, I'll label the angles in each case T and P as shown in my diagram)

Let the velocity of the wind relative to the car be V_wc then:

V_wc = V_w - V_c

therefore V_w = V_wc + V_c

This is the true velocity of the wind.

In the first situation call the apparent magnitude of the wind's velocity K1 and in the second call it K2 then:

Now I can eliminate K1 and solve for K2, I get:

K2 = 2u / ( cos(P) tan(T) - sin(P) )

I can substitute this into the Case 2 equation for V_w to obtain:

V_w =

So this is the true velocity of the wind.

So now, for case 3 where the speed of the motorist is 2u heading north I need to find:

V_wc = V_w - V_c =

This leads to :

2 tan(w) =

Which is not the desired answer.

Thanks for any help,

Mitch.

Here's my attempt: (i and j are unit vectors in the directions of east and north respectively)

(apologies that LaTeX is simply not working for me, I'll label the angles in each case T and P as shown in my diagram)

Let the velocity of the wind relative to the car be V_wc then:

V_wc = V_w - V_c

therefore V_w = V_wc + V_c

This is the true velocity of the wind.

In the first situation call the apparent magnitude of the wind's velocity K1 and in the second call it K2 then:

__Case 1:__V_w = -K1 * cos(T) i + ( K1 * sin(T) - u ) j__Case 2:__V_w = -K2 * cos(P) i + ( K2 * sin(P) + u ) jNow I can eliminate K1 and solve for K2, I get:

K2 = 2u / ( cos(P) tan(T) - sin(P) )

I can substitute this into the Case 2 equation for V_w to obtain:

V_w =

**(**-2u / [ tan(T) - tan(P) ]**)**i +**(**2u / [ tan(T) tan(P) - 1 ] + u**)**jSo this is the true velocity of the wind.

So now, for case 3 where the speed of the motorist is 2u heading north I need to find:

V_wc = V_w - V_c =

**(**-2u / [ tan(T) - tan(P) ]**)**i +**(**2u / [ tan(T) tan(P) - 1 ] - u**)**jThis leads to :

2 tan(w) =

**(**( 2 / [ tan(T) tan(P) - 1 ] - 1 )**)*** (tan(T) - tan(P))Which is not the desired answer.

Thanks for any help,

Mitch.