A kid at the junior high cafeteria wants to propel an empty milk carton along a lunch table by hitting it with a 3.1 g spit ball. part a if he wants the speed of the 20 g carton just after the spit ball hits it to be 0.28 m/s, at what speed should his 3.1 g spit ball hit the carton?

Does the spit ball stick to the carton once it hits? assuming this, we solve this problem using conservation of momentum

the momentum of the spitball/carton system before collision is the same as the momentum after collision

momentum before collision = 0.0031kgxV where V is the initial speed of the spitball

momentum after collision = 0.0231kgx0.28m/s = 0.006468 kgm/s

(note that the mass after collision is the sum of the carton and spitball)

solving for V gives:

V = 0.006468 kgm/s / 0.0031kg = 2.09 m/s

answer

his 3.1 g spit ball should hit the carton at 2.09 m/s

We answer this problem using conservation of momentum

the momentum of the spitball/carton system before collision is the alike as the momentum after the collision

momentum before collision = 0.0031 kg x V, the v here is the initial speed

momentum after collision = 0.0221kg x 0.28m/s = 0.0062 kg m/s

(note that the mass after collision is the sum of the carton and spitball)

solving for V gives:

V = 0.0062 kg m/s / 0.0221 kg = 0.280542986 m / s