Homework Help: Momentum - Exploding Apart

1. Jan 25, 2009

tornzaer

1. The problem statement, all variables and given/known data

A grenade of mass 1.2 kg is at rest on a smooth frictionless surface when it suddenly explodes into three pieces. A 0.5 kg piece flies off horizontally to the north at 3.0 m/s, a 0.3 kg piece flies off horizontally to the southwest at 4.0 m/s. What is the speed and direction of the third piece?

2. Relevant equations

P=mv P123=P1+P2+P3 Cosine Law

3. The attempt at a solution

Well, I know the mass and velocity of the first two pieces. I know the mass of the third piece due to the remaining mass from the total and it comes up to 0.4 kg. I know the momentum of the first two pieces. I know I have to draw a diagram and find the momentum of the unknown side, which would be P1+P2. Then, I can solve for v3 by dividing m3 from P1+P2. The problem, however is the direction. Since the second piece flies southwest, I'm assuming the angle is 45 degrees. That leaves me with two unknown angles. I can find this by using the Sine Law, but I don't know which angle to use.

This is where I need help, what is the direction of the third piece? Could someone please show me the diagram and which angle would be it for the third piece. Just as a side note, the velocity of the third piece comes up to a negative number, so does that mean that the direction will be switched? Thank you very much for the help. This is for my exam that's tomorrow.

2. Jan 25, 2009

Delphi51

The momentum before the explosion is zero - in the east/west direction AND in the north/south direction. Make two headings for the two directions and then write
0 = p1 + p2 + p3 for each. Put in the known quantities, using 4*cos(45) for the east/west part of the velocity of the 2nd piece. I expect you will have two equations with two unknowns - the speed and angle of the 3rd piece. Solve the system of equations to find them.

3. Jan 25, 2009

tornzaer

Hmmm... Is there a way to solve it by drawing a single triangle? Then I could use the cosine law to find the one side and the sine law from thereon to find the angle of the direction I need. This is how we've done it thus far in class. It's just that I don't know which of the two blank angles is the directional angle. I could use sine law to find either one, just don't know which one.

Thanks.

4. Jan 25, 2009

LowlyPion

It's much easier to just sum the X-components and Y-components as already suggested.

You end with the numerical values of the x,y of the third piece directly. Then combine them for the |magnitude| and use the tan-1 to get the angle directly.