- #1

Aurelius120

- 251

- 24

- Homework Statement
- Two cars are moving at constant speed one on a circular track and other on horizontal path. Radius of circular track is 200m. The magnitude of relative velocity is graphed as follows. Find their speeds

- Relevant Equations
- $$v_{rel}=v_A-v_B$$

In the question I assumed the velocity of the circular object to be :

$$\vec v_A= v cos( \phi + \omega t) \hat i + v sin(\phi + \omega t) \hat j$$

where $$\omega = \frac{v}{R}$$

Velocity of the other particle is

$$\vec v_B = v \hat i$$

Now magnitude of relative velocity comes out on evaluation to be

$$v_{rel} = \sqrt {2v^2(1-cos(\phi+\omega t)}$$

On further solving, by using

##v_{25}=0## and ##v_{0}=v_{50}##

I couldn't solve further and my whatever little solving I did gave incorrect answers.

**So, Is my method correct? If yes then how do I proceed further?**

I noticed a second method that simply took

*relative velocity to be maximum when both were moving in opposite directions and since that value was 40 the value of individual speeds must be 20*. I could consider it a correct method if I let the fact that the graph doesn't touch 40 slide.

**But that leaves another problem ##2 \pi R= 2×200× \pi= 20×50## which is not correct.**

Please help. Thank you

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