these questions have to do with conservation of momentum, i gave an example to better understand how to do it below. Please show all your work to the answers so i can understand thank you.

ex: A bomb initially at rest on a smooth, horizontal surface is exploded into three pieces. Two pieces fly off at a 90^o angle to each other, a 2.0 kg piece at 20 m/s and a 3.0 kg piece at 12 m/s. The third piece flies off at 30 m/s.

(a) Determine the momentum and the direction of motion of the third piece. (b) What is its mass? Answers: (a) 53.8 kgm/s;42^obelow the horizontal (b) 1.8 kg

Questions:

1) An 8.0 kg mass collides elastically with a 5.0 kg mass that is at rest. Initially, the 8.0 kg mass was traveling to the right at 4.5 m/s. After the collision, it is moving with a speed of 3.65 m/s and at an angle of 27 to its original direction. What is the final speed and direction of motion for the 5.0 kg mass?

2) A bomb originally at rest explodes into three pieces, all of the same mass. One mass flies North at 80 m/s and a second mass moves East at 60 m/s. Determine the velocity of the third mass.

3)A 1325 kg car (C) moving north at 27.0 m/s collides wit ha 2165 kg car (D) moving east at 11.0 m/s. The two cars are stuck together. In what direction and with what speed do they move after the collision?