Question

An object located at the origin and having mass M explodes into three pieces having masses M/4, M/3, and 5M/12. The pieces scatter on a horizontal frictionless xy-plane. The piece with mass M/4 files away with velocity 5.0 m/s at
37∘
above the x-axis. The piece with mass M/3 has velocity 4.0 m/s directed at an angle of
45∘
above the -x-axis. (a) What are the velocity components of the third piece? (b) Describe the motion of the CM of the system after the explosion.

Answer 1

Too complicated to do here, but here is the method.
Use conservation of momentum, in x and y directions.
Because the initial momenum, in x and y, was zero...
break each piece into x and y components of momentum.
add the momentumX and set to zero, same as momentumY set to zero.
you have two equations, two unknowns (velocities). Solve

Answer 2

Ok...I got that the angle theta from the positive x-axis is = 268 degrees (for the third piece).
Am I on the right track? Thank you!

Answer 3

55