Question

If you toss a ball upward, is the momentum of the moving ball conserved? Explain.

Answer 1

Momentum = mass * velocity = Impulse = Force * time

You, the ball and the earth have 0 momentum. You throw the ball up your force on the ball for the time it takes to throw the ball equals the momentum of the transferred leaves your hands. The ball goes up it loses velocity that loss is exactly balanced by the force of gravity for the time the ball rises. The momentum of the ball is transferred to the earth through that impulse.

.The ball starts back down. Gravity still acts on the ball for the time it falls. The velocity of the ball increases and that impulse adds velocity to the ball. The earth is losing the momentum it gained when the ball went up. Finally, you catch the ball absorbing all the momentum it gained falling and your impulse stopping the ball exactly balances and the total momentum of you, the ball, and the earth returns to 0 which is what it was before you threw the ball.

If a ball in a flight is thrown upward then momentum is not conserved. The Earth is imparting a constant force on it (in the Newtonian framework) from outside the system, so its momentum is changing.