A pilot drops a bomb from a plane flying horizontally with constant velocity. When the bomb hits the ground, the horizontal location of the plane will
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Answer: When the pilot drops a bomb from a plane flying horizontally with constant velocity, the horizontal location of the plane at the moment the bomb hits the ground will be directly above the impact point. This occurs because the bomb will continue to possess the horizontal component of the plane's velocity even after it's been released.
Here are the logical steps to understand this phenomenon:
1. **Horizontal Motion & Vertical Motion Are Independent:** According to the principles of physics, specifically Newton's first law of motion, an object in motion will continue in motion at a constant velocity unless acted upon by an external force. This applies separately to horizontal and vertical motion - they do not affect each other.
2. **Initial Motion:** When the bomb is released, it has two components of motion - the forward (horizontal) motion that it shares with the plane, and any vertical motion it gains after release due to gravity.
3. **Gravity's Role:** Gravity acts only in the vertical direction and does not affect the horizontal velocity of the bomb. Therefore, the bomb accelerates downward due to gravity, but its horizontal velocity remains constant (the same as the plane's) because there is no horizontal force acting on it.
4. **Trajectory of the Bomb:** The result is that the bomb follows a parabolic trajectory as it falls. This trajectory is the result of the bomb's constant horizontal velocity paired with its increasing vertical velocity due to gravity.
5. **Plane’s Location At Impact:** Since the bomb retains the plane's horizontal velocity, the plane will be directly above the spot where the bomb hits the ground if the plane continues its flight with the same speed and direction.
It's important to note that this explanation assumes no air resistance or any other forces acting on the bomb other than gravity.