1. ## relative velocity

two planes A and B are flying at the same height. A is travelling at 500 km hr^-1 in a westerly direction. B is travelling at 600 km hr^-1 in a north westerly direction. a third plane C is also flying at the same flying at the same height appears to pilot A to be flying in a north west direction. whereas to the pilot of B plane C appears to be flying in a direction 30 degrees south of west. find the magnitude and direction of the true velocity of plane C

i have tried solving this using the 2 formula Vca=Vc-Va and Vcb=Vc-Vb but there are too many variables.

2. ## Re: relative velocity

... another one of these?

I get $|v_c| \approx 780 \, km/hr$, direction of about $18^\circ$ N of W

3. ## Re: relative velocity

its a little different from the last one .yes that is correct.

how did you do it?

4. ## Re: relative velocity

Law of Sines to form two equations (see attached vector diagram)

upper triangle ...

$\dfrac{V_C}{\sin(105^\circ)} = \dfrac{V_B}{\sin{\theta}} \implies V_C = \dfrac{V_B\sin(105^\circ)}{\sin{\theta}}$

lower triangle ...

$\dfrac{V_C}{\sin(135^\circ)} = \dfrac{V_A}{\sin(75^\circ -\theta)} \implies V_C = \dfrac{V_A\sin(135^\circ)}{\sin(75^\circ -\theta)}$

set the two expressions for $V_C$ equal & solved for $\theta$ ... then determined $V_C$

5. ## Re: relative velocity

i understand the problem now . thank you. your method cuts out all the variables i had as i was working from two seperate diagrams