vectors at t<0

Printable View

July 3rd 2008, 02:56 AM
thermalwarrior

vectors at t<0

I have the following information:

A particle A of mass m is moving along a smooth horizontal surface with velocity of 2i + 3j. A second particle of mass 3m is moving with velocity 6i - 5j, collides with A at the origin at t=0. After this the particles coalesce.

question:

Find the expressions of Ra(t) and Rb(t), the respective position vectors of the particles A and B at time <0. Hence find the position vector of the centre of mass of the system before the collision. Hence determine the velocity of the centre of mass.

how do i go about this?

cheers
July 3rd 2008, 03:37 AM
mr fantastic

Quote:

Originally Posted by thermalwarrior

I have the following information:

A particle A of mass m is moving along a smooth horizontal surface with velocity of 2i + 3j. A second particle of mass 3m is moving with velocity 6i - 5j, collides with A at the origin at t=0. After this the particles coalesce.

question:

Find the expressions of Ra(t) and Rb(t), the respective position vectors of the particles A and B at time <0. Hence find the position vector of the centre of mass of the system before the collision. Hence determine the velocity of the centre of mass.

how do i go about this?

cheers

This should get you started:

Particle A: $v_A = \frac{d r_A}{dt} = 2 i + 3 j \Rightarrow r_A(t) = (2t + C_1) i + (3t + C_2) j, ~ t \leq 0$ .

But $r_A(0) = 0 i + 0 j \Rightarrow C_1 = C_2 = 0$ .

Therefore $r_A(t) = (2t) i + (3t) j, ~ t \leq 0$ .
July 3rd 2008, 03:42 AM
mr fantastic

Quote:

Originally Posted by thermalwarrior

I have the following information:

A particle A of mass m is moving along a smooth horizontal surface with velocity of 2i + 3j. A second particle of mass 3m is moving with velocity 6i - 5j, collides with A at the origin at t=0. After this the particles coalesce.

question:

Find the expressions of Ra(t) and Rb(t), the respective position vectors of the particles A and B at time <0. Hence find the position vector of the centre of mass of the system before the collision. Hence determine the velocity of the centre of mass.

how do i go about this?

cheers

This question links rather nicely with the one in this thread: http://www.mathhelpforum.com/math-he...-momentum.html
July 3rd 2008, 09:42 AM
thermalwarrior

so im correct in understanding from that reply the conditions at t=0 will hold for t<0?

to find the centre of mass of the system could i assume that the two particles are joined some kind of rod to make the system whole or can i just use the equation for centre of mass:

r = m1r1 + m2r2/m1+m2

then differentiate the position vector to find the velocity???