Relative Velocity of P & Q: Magnitude & Direction

[thereddevils]

Homework Statement

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 .

Homework Equations

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 ?

 

[tiny-tim]

Hi thereddevils!

(have a pi: π and try using the X² tag just above the Reply box )

|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 ?

(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) …

 

[thereddevils]

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) …

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

 

[tiny-tim]

I think your calculator is wrong.

 

[thereddevils]

I think your calculator is wrong.

lol ! , its in radians mode

thanks a lot !