Question

A bomb is dropped by a fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a :

• A. parabola in the direction of motion of plane
• B. straight line vertically down the plane
• C. parabola in a direction opposite to the motion of plane
• D. hyperbola

Hint:

In problems of relative motion, always identify the frame of reference. For an object dropped from a vehicle moving with constant velocity (neglecting air resistance), the object's horizontal velocity remains the same as the vehicle's. Thus, from the vehicle's perspective, there is no horizontal motion, only vertical motion.

Answer 1

The Correct Option is B

To solve the given problem, we need to analyze the motion of a bomb dropped from an aircraft moving horizontally. This involves understanding the principles of motion in physics, specifically the concepts of projectile motion and the observer's frame of reference.

Let's break this down step-by-step:

1. When a bomb is dropped from a plane flying horizontally, it initially has the same horizontal velocity as the plane. This is due to the principle of inertia; the bomb retains the horizontal motion of the plane.
2. In the absence of air resistance, the only force acting on the bomb after it is released is gravity, which accelerates it downward.
3. From the ground observer’s frame of reference, the bomb follows a parabolic trajectory due to its initial horizontal velocity and constant vertical acceleration (gravity).
4. However, the question specifically asks for the trajectory as seen by an observer sitting in the plane.
5. In the plane's frame of reference, the horizontal motion of the plane and the bomb are the same. Since their horizontal velocities are equal, the horizontal component of motion cancels out for this observer.
6. Therefore, the observer in the plane perceives only the vertical component of motion. The bomb appears to fall straight down beneath the plane.

Given this understanding, let's evaluate the provided options:

1. Parabola in the direction of motion of the plane: This would be true for a ground observer, not for someone inside the plane.
2. Straight line vertically down the plane: This is the correct choice as explained above.
3. Parabola in a direction opposite to the motion of the plane: This is irrelevant as the horizontal velocity does not change direction.
4. Hyperbola: This is not applicable in this situation.

Thus, the correct answer is: Straight line vertically down the plane.