Particle projection, momentum. Somewhat .

[Maybe_Memorie]

Particle projection, momentum. Somewhat urgent.

Homework Statement

I didn't properly explain myself last time. I've included a diagram for reference.

Two particle of masses m and 3m are connected by a light rigid rod. The system rests on a smooth horizontal table, the heavier mass due east of the lighter mass. The heavier mass is projected with initial velocity $$u j^>$$. Find the velocities of the particles when the rod runs north-south.

Homework Equations

Energy, momentum.

The Attempt at a Solution

I applied momentum to the upward direction, and then applied conservation of energy. I end up with too many variable and am quite unsure how to solve this problem. any hints would be greatly appreciated.

 

[jbsteele]

Let's denote the masses by m and 3m and the velocities after the collision as v1 and v2. We can write the equations of conservation of momentum and energy, respectively, as follows:Momentum: mv1 + 3mv2 = muEnergy: (1/2)mv1^2 + (1/2)3mv2^2 = (1/2)mu^2Combining these two equations and solving for v2, we get:v2 = (mu - mv1)/3mSubstituting this expression for v2 into the momentum equation, we get:mv1 + 3(mu - mv1)/3m = muSolving for v1, we get:v1 = (2/4)muFinally, substituting this expression for v1 into the equation for v2, we get:v2 = (2/12)muTherefore, the velocities of the particles when the rod runs north-south are (2/4)mu and (2/12)mu.