Jake is bowling with a 8 kg bowling ball. he rolls the ball at 7 m/s, and it hits one stationary pin with a mass of 2 kg. the pin goes flying forward at 12 m/s. how fast is the bowling ball now traveling?

We know from the principle of conservation of momentum that the momentum of the system is conserved. the total momentum of the system is 8  kg x 7 m/s = 56 kg m/s. the momentum of the pin after getting hit is 24 kg  m/s. so the momentum of the bowling ball after hitting the pin is 56 kg m/s - 24 kg m/s = 32 kg m/s
velocity of the ball is v = 32 kg m/s / 8 kg = 4 m/s