What is the mass and direction of the third piece?

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The problem involves a rubber block that explodes into three pieces, with two pieces having known masses and velocities. A 200g piece moves at 1.4 m/s and a 300g piece at 0.90 m/s, with an angle of 80 degrees between their trajectories. To find the mass and direction of the third piece, a momentum conservation approach is necessary, considering both the x and y components of momentum. The total momentum before and after the explosion must be equal, allowing for the calculation of the unknown mass and direction of the third piece. A detailed body diagram is suggested to visualize the problem and assist in the calculations.
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Homework Statement


A small explosive charge is placed in a rubber block resting on a smoother surface(frictionless). when the charge is detonated, the block
breaks into three pieces. A 200g piece travels 1.4 m/s and 300g piece travels at 0.90m/s. The third piece flies off at a speed of 1.8m/s.
If the angle between the first two pieces is 80(degrees), calculate the mass and the direction of the third piece. two sig figs.

Homework Equations


n/a


The Attempt at a Solution


honestly no idea. Help would be wonderfull
 
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First start is the body diagram. Indicate what you know from the problem.
 
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