An object with total mass mtotal = 14.3 kg is sitting at rest when it explodes into three pieces. One piece with mass m1 = 4.7 kg moves up and to the left at an angle of θ1 = 24° above the –x axis with a speed of v1 = 25.8 m/s. A second piece with mass m2 = 5.4 kg moves down and to the right an angle of θ2 = 29° to the right of the -y axis at a speed of v2 = 22.3 m/s. 1)What is the magnitude of the final momentum of the system (all three pieces)?

The equation to find momentum is [tex]P=mV[/tex]. Also, momentum is conserved. So before and after the explosion the momentum should be the same.

Since the object sitting at rest initially its momentum is [tex]P_{before} =14,3.0=0[/tex]

Since [tex]P_{before} =P_{after}[/tex] → [tex]P_{after} =0[/tex]

Also because it explodes into 3 pieces, the total momentum of this 3 pieces should be [tex]P_{after} =P_{1} +P_{2} +P_{3} =0[/tex]

Since we can calculate [tex]P_{1}[/tex] and [tex]P_{2}[/tex] because we know their mass and the speed, we can calculate the final momentum [tex]-P_{3} =P_{1} +P_{2}[/tex]

[tex]-P_{3} =4,7.25,8+5,4.22,3[/tex] → [tex]-P_{3} =241,68kgm/s[/tex]

[tex]P_{3}[/tex] being negative shows that the third piece moves up to the opposite way from the other two object. As we are asked to find the magnitude, the answer is found upwards.