# Relative velocity

1. May 14, 2010

### thereddevils

1. The problem statement, all variables and given/known data

A particle , P moves on a horizontal plane along the circumference of a circle with centre O and a radius of 3m at an angular velocity of pi/4 rad/s in the clockwise direction . A second particle , Q moves on the same plane along a circle with radius 2m and the same centre as the first circle at an angular velocity of pi/2 rad/s in the clockwise direction . At first , O, P and Q are collinear with P and Q located at the north of O . Find the magnitude and direction of the velocity of P relative to Q .

2. Relevant equations

3. The attempt at a solution

the angular displacement of P and Q are 3pi/4 and 3pi/2 respectively .

The linear velocities of P and Q are 3pi/4 and pi respectively .

then one of the angle of the triangle is 3pi/4

so i can use the cosine rule ,

|pVq|^2=pi^2+(3pi/4)^2-2pi(3pi/4)cos (3pi/4)

|pVq|=5.49 m/s

bu the answer given is 5.09 m/s

where did i go wrong ?

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2. May 14, 2010

### tiny-tim

Hi thereddevils!

(have a pi: π and try using the X2 tag just above the Reply box )
(i assume this is to be calculated after 3 seconds?)

General tip: take out any awkward factors first … then you're less likely to make mistakes, and if you do make one, you're more likely to see where it is.

Then your equation is (π/4)2 times (9 + 16 + 2*3*4*1/√2) = (π/4)2(25 + 12√2) …

3. May 14, 2010

### thereddevils

thanks tiny , is my mistake in the calculation in the cosine rule , or the diagram is wrong ?

4. May 14, 2010

### tiny-tim

I think your calculator is wrong.

5. May 14, 2010

### thereddevils

lol !!!!!! , its in radians mode :grumpy:

thanks a lot !!