Solving Exercise: Finding Velocity Vector of Cyclist

[Azeri]

Hi! I have an exercise here that I can't solve. Help please.

"One of two cylists cycles in the north-west direction at a speed of 8 m/s making an angle of 53 with the west. The other cyclist cycles in north-east direction at a speed of 6m/s making an angle of 37 with the east. How does the second cyclist see the motion of first one?" (magnitude of velocity vector and direction)

Thanks... :

 

[jcsd]

As usual show us what you've done.

The obvious starting point is: What is the angle between the two cyclists?

 

[Azeri]

It must be 90

 

[jcsd]

Yes, so what will the coponents of the relative velocity of the first cyclist (to the second cyclist)

a) along his (the second cyclist's) diretcion of travel

b) 90 degrees to his direction of travel

 

[Azeri]

I've found all Vx and Vy 's and Vrelative is 10m/s to North -West. But the answer in book is 10m/s to North-east

 

[jcsd]

It sounds to me is what you've done is forgotten that the component of the first cyclist's velocity (relative to the second cyclist) along the the second cyclist's axis will be opposite and equal to the second cyclist's actual velocity.

 

[Doc Al]

I've found all Vx and Vy 's and Vrelative is 10m/s to North -West. But the answer in book is 10m/s to North-east

Your answer makes sense to me. Since they are separating along the east-west axis, the relative velocity (of the first with respect to the second) must have a westward component.

 

[Azeri]

I use this formula: Vrelative=Vc1-Vc2

 

[Doc Al]

Vrelative=Vc1-Vc2

That is correct.

 

[Azeri]

Thanks. Now I am sure about my answer.