Question

a kid at the junior high cafeteria wants to propel an empty milk carton along a lunch table by hitting it with a 3.0 g spit ball. if he wants the speed of the 20 g carton just after the spit ball hits it to be 0 . 30 m / s , at what speed should his spit ball hit the carton?

Answer 1

To find the speed at which the spit ball should hit the milk carton, we can use the principle of conservation of momentum. The spit ball should hit the carton with a velocity of approximately 0.307 m/s.

Step-by-step explanation:

To find the speed at which the spit ball should hit the milk carton, we can use the principle of conservation of momentum. The momentum of an object is the product of its mass and velocity. In this case, we have an empty milk carton with a mass of 20 g (0.020 kg) and a desired final speed of 0.30 m/s. The spit ball has a mass of 3.0 g (0.003 kg).

According to the conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Mathematically, this can be written as:

m1v1 + m2v2 = m1vf + m2vf

Since the milk carton is initially at rest, its initial velocity (v1) is 0. The spit ball's initial velocity (v2) is what we need to find. Rearranging the equation, we get:

m2v2 = m1vf + m2vf

Plugging in the values, we have:

(0.003 kg)(v2) = (0.020 kg)(0.30 m/s) + (0.003 kg)(0.30 m/s)

Solving for v2, we find that the spit ball should hit the milk carton with a velocity of approximately 0.307 m/s.