A small bag of sand is released from a hot air balloon that is ascending vertically at a constant velocity. Ignoring air resistance, what is the initial velocity of the sand bag immediately after it is released, relative to the ground?

• A. Downward, equal to the velocity of the balloon
• B. Upward, but less than the velocity of the balloon
• C. Upward, equal to the velocity of the balloon
• D. $0$ (the sand bag starts from rest relative to the ground)

Answer: (C)

Verified step by step guidance

1. Understand the scenario: A hot air balloon is ascending vertically at a constant velocity, and a small bag of sand is released from it.
2. Recall the principle of relative velocity: When an object is released from a moving platform, its initial velocity relative to the ground is the same as the velocity of the platform at the moment of release, assuming no external forces like air resistance act immediately.
3. Since the balloon is moving upward at a constant velocity, the sand bag, at the instant it is released, will have the same upward velocity as the balloon relative to the ground.
4. Therefore, the initial velocity of the sand bag relative to the ground is upward and equal in magnitude to the velocity of the balloon.
5. After release, the sand bag will begin to accelerate downward due to gravity, but its initial velocity at the moment of release matches the balloon's upward velocity.