1. ## 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

2. 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 $r_A(t) = (2t) i + (3t) j, ~ t \leq 0$.

3. 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.