A bomb is dropped from a plane travelling horizontally with uniform...

Let the velocity of the plane be $\vec{v} = v_x \hat{i} + v_y \hat{j}$. Since the plane moves with uniform velocity, its horizontal and vertical displacements at any time $t$ are $x_p = v_x t$ and $y_p = v_y t$.

When the bomb is dropped, it inherits the initial velocity of the plane. The horizontal velocity of the bomb remains constant because there is no horizontal acceleration (neglecting air resistance). Its horizontal displacement at time $t$ is $x_b = v_x t$.

The vertical displacement of the bomb under gravity is $y_b = v_y t - \dfrac{1}{2} g t^2$.

Since $x_p = x_b$ at all times, the bomb will always be exactly vertically below the plane.

This result depends only on the horizontal component of the velocity being constant and equal for both the plane and the bomb. It is independent of the vertical component of the plane's velocity $v_y$. Therefore, the conclusion remains true even if the plane travels with uniform speed in a non-horizontal straight line.