A cherry bomb explodes into three pieces of equal mass. One piece has an initial velocity of 12m/sx^. Another piece has an initial velocity of 7.0m/sx^−5.0m/sy^.


Part A
What is the velocity of the third piece?
Enter the x and y components of the velocity separated by a comma. Express your answer

To find the velocity of the third piece, we can use the principle of conservation of momentum. According to this principle, the total momentum before the explosion should be equal to the total momentum after the explosion.

Let's denote the mass of each piece as m, and the initial velocity of the third piece as V.

Before the explosion, the total momentum is given by the sum of the momentum of each piece:

Initial momentum = m * (12m/sx^) + m * (7.0m/sx^−5.0m/sy^)

Since each piece has an equal mass, we can simplify this expression:

Initial momentum = 12m^2/s + 7.0m^2/s - 5.0m^2/sy^

After the explosion, the momentum of the first piece can be calculated using its mass and initial velocity:

Momentum of first piece = m * (12m/sx^)

The momentum of the second piece can be calculated similarly:

Momentum of second piece = m * (7.0m/sx^−5.0m/sy^)

The momentum of the third piece will be:

Momentum of third piece = m * V

According to the conservation of momentum principle, the sum of the momenta after the explosion should be equal to the sum of the momenta before the explosion:

Initial momentum = Momentum of first piece + Momentum of second piece + Momentum of third piece

Substituting the values we have:

12m^2/s + 7.0m^2/s - 5.0m^2/sy^ = m * (12m/sx^) + m * (7.0m/sx^−5.0m/sy^) + m * V

Now, to solve for V, we need to isolate it on one side of the equation. We can start by combining like terms:

12m^2/sx^ + 7.0m^2/sx^−5.0m^2/sy^ = 12m + 7.0m - 5.0m/sy^ + V

Next, we can move the known terms to the other side of the equation:

V = 12m + 7.0m - 5.0m/sy^ + 12m^2/sx^ + 7.0m^2/sx^−5.0m^2/sy^

Simplifying further if necessary will give you the solution for V, with the x and y components separated by a comma.