# vectors at t<0

• Jul 3rd 2008, 03:56 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.

cheers
• Jul 3rd 2008, 04:37 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.

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 $r_A(t) = (2t) i + (3t) j, ~ t \leq 0$.
• Jul 3rd 2008, 04:42 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.

cheers

This question links rather nicely with the one in this thread: http://www.mathhelpforum.com/math-he...-momentum.html
• Jul 3rd 2008, 10:42 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???