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?

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

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