An object with total mass mtotal = 17.3 kg is sitting at rest when it explodes into three pieces. One piece with mass m1 = 4.9 kg moves up and to the left at an angle of θ1 = 20° above the –x axis with a speed of v1 = 25.6 m/s. A second piece with mass m2 = 5.1 kg moves down and to the right an angle of θ2 = 25° to the right of the -y axis at a speed of v2 = 21 m/s.

a.) The magnitude of the final momentum is zero.
b.) The mass of the third piece is 7.3kg
c.) What is the x-component of the velocity of the third piece?
d.) What is the y-component of the velocity of the third piece?

Question

An object with total mass mtotal = 17.3 kg is sitting at rest when it explodes into three pieces. One piece with mass m1 = 4.9 kg moves up and to the left at an angle of θ1 = 20° above the –x axis with a speed of v1 = 25.6 m/s. A second piece with mass m2 = 5.1 kg moves down and to the right an angle of θ2 = 25° to the right of the -y axis at a speed of v2 = 21 m/s.

a.) The magnitude of the final momentum is zero.
b.) The mass of the third piece is 7.3kg
c.) What is the x-component of the velocity of the third piece? 
d.) What is the y-component of the velocity of the third piece?

aravindg · Answer

The center of mass of the system remains at rest. Use it here.

theeric · Answer

And you can also use the conservation of momentum. So the mass times velocity for the pieces has to add up to zero!

And mass is conserved. So the mass of the pieces must add to the mass that they had together.

theeric · Answer

The rest will involve breaking up the velocities into components like you might be used to doing with forces.