A 2.40 kgkg can of coffee moving at 1.50 m/sm/s in the +x+x-direction on a kitchen counter collides head-on with a 1.20 kgkg box of macaroni that is initially at rest. After the collision the can of coffee is moving at 0.825 m/sm/s in the +x+x-direction. What is the velocity (magnitude and direction) of the box of macaroni after the collision? Express your answer to three significant figures and include the appropriate units. Enter positive value if the box is moving in the +x+x-direction and negative value if the box is moving in the −x−x-direction.

1.35 m/s in the +x direction

Explanation:

Mass of can of coffee, m = 2.4 kg

Initial velocity of can of coffee, u = 1.5 m/s

Mass of box of macaroni, M = 1.2 kg

Initial velocity of box of macaroni, U = 0 m/s

Final velocity of can of coffee, v = 0.825 m/s

We can find the final velocity of the box of macaroni, V, by using the Principle of Conservation of momentum:

Total initial momentum = Total final momentum

Momentum is given as the product of mass and velocity. Hence:

mu + MU = mv + MV

(2.4 * 1.5) + (1.2 * 0) = (2.4 * 0.825) + (1.2 * V)

3.6 + 0 = 1.98 + 1.2V

1.2V = 3.6 - 1.98 = 1.62

=> V = 1.62/1.2

V = 1.35 m/s

The final velocity of the box of macaroni is 1.35 m/s and it is in the +x direction.

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