Animated Solution for Physics - Kinematics: A bomb is dropped by fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a

Imagine you are a pilot flying a fighter plane horizontally at a constant, blistering speed. You press a button, and a bomb is released from the bay doors. What happens next? How does the bomb fall? The answer depends entirely on who is asking the question.

This classic physics problem beautifully illustrates the concept of relative velocity and the power of frames of reference.

Let's first look at this from the perspective of someone standing on the ground. When the bomb is released, it doesn't just drop straight down. Because of inertia, it retains the horizontal velocity of the plane at the exact moment of release.

Let's define the velocity of the plane as ${\vec{v}}_p=v_x\hat{i}$.

The moment the bomb is dropped, its initial velocity with respect to the ground is also $v_x\hat{i}$. However, gravity immediately begins to pull it downwards, giving it an increasing vertical velocity component, $-v_y\hat{j}$.

So, the velocity of the bomb with respect to the ground at any time $t$ is:

Because the bomb is moving forward at a constant speed while accelerating downwards, it traces out a curved path. To the ground observer, the trajectory is a perfect parabola.

Now, let's jump back into the cockpit. The pilot is moving horizontally at the exact same speed as the bomb's horizontal component. To find out what the pilot sees, we must calculate the relative velocity of the bomb with respect to the plane.

The formula for relative velocity is:

Let's substitute our vectors into this equation:

Notice the magic of algebra here! The horizontal components perfectly cancel each other out:

The relative velocity vector ${\vec{v}}_{bp}$ has absolutely no horizontal component ($\hat{i}$). It only has a vertical component pointing downwards ($-\hat{j}$).

What does this mean physically? It means that from the pilot's perspective, the bomb is not moving forward or backward at all. It is simply falling straight down, directly beneath the plane. Therefore, to an observer sitting in the plane, the trajectory of the bomb is a straight line vertically down the plane.

This problem is a fantastic reminder that motion is always relative. A parabola to one person can be a straight line to another, and both are completely correct in their own frames of reference!