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An object with total mass mtotal = 16.6 kg is sitting at rest when it explodes into three pieces. One piece with mass m1 = 5 kg moves up and to the left at an angle of θ1 = 25° above the –x axis with a speed of v1 = 27 m/s. A second piece with mass m2 = 5.4 kg moves down and to the right an angle of θ2 = 30° to the right of the -y axis at a speed of v2 = 21.8 m/s. What is the x-component of the velocity of the third piece? What is the y-component of the velocity of the third piece? What is the magnitude of the velocity of the center of mass of the pieces after the collision?

2. Homework Equations

I know that for both components, the velocities of all three masses equal 0 when added together (v1_x+v2_x+v3_x=0 and same for y component). I know how to solve for the center of mass using the velocities but I need to figure out the velocity components of the third mass first.

3. The Attempt at a Solution

I've tried this many ways but the one that seems correct to me would be...

v1_x = -27 m/s * cos (25) =-24.47 m/s

v2_x = 21.8 m/s * sin (30) = 10.9 m/s

v3_x = -v1_x - v2_x = 24.47 m/s - 10.9 m/s = 13.57 m/s

v1_y = 27 m/s * sin (25) = 11.41 m/s

v2_y = -21.8 m/s * cos (30) = -18.88 m/s

v3_y = -v1_y - v2_y = -11.41 m/s + 18.88 m/s = 7.47 m/s

However, none of these answers are correct according to the program I am using.