Question

14. A firecracker stuck into a 150 g apple explodes and sends five apple fragments in different directions. The vector sum of momenta 1, 2, 3, and 4 is found from a video of the event to have components px = 1.20 kg*m/s, py = 0.80 kg*m/s (with no other component). The mass of the fifth fragment is 0.050 kg. What is its velocity right after the explosion?

Answer 1

Momentum P(1-4) = 1.2 X + 0.8 Y [kg m/s] where X and Y are unit vectors in those directions. By conservation of momentum, momentum of fragment 5 = -1.2X - 0.8 Y [kg m/s]. P(5)=M(5)*V(5); v(5)=P(5)/M(5) = (-1.2 X - 0.8 Y kg m/s)/0.05 kg = -24 X - 16 Y [m/s].

In summary, for fragment 5, vx=-24 m/s; vy=-16 m/s