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

The bomb is dropped from a fighter plane flying in horizontal direction only.

Let us assume the velocity of fighter plane, ${\mathbf{v}}_{\mathrm{a}}={\mathrm{v}}_{\mathrm{x}}\hat{\mathrm{i}}$. As fighter plane is moving in horizontal direction only. Hence, it has only one component.

When fighter plane drops the bomb, the bomb will free fall from the fighter plane and have a horizontal velocity in the direction of plane and vertical velocity due to gravity.

Velocity of bomb can be given as, ${\mathbf{v}}_{\mathrm{b}}={\mathrm{v}}_{\mathrm{x}}\hat{\mathrm{i}}-{\mathrm{v}}_{\mathrm{y}}\hat{\mathrm{j}}$. Velocity in vertical direction will be negative as bomb is moving downwards.

Now, for the person sitting inside the plane, hence the relative velocity of bomb with respect to plane can be calculated as

           ${\mathrm{v}}_{\mathrm{ba}}={\mathrm{v}}_{\mathrm{b}}-{\mathrm{v}}_{\mathrm{a}}={\mathrm{v}}_{\mathrm{x}}\hat{\mathrm{i}}-{\mathrm{v}}_{\mathrm{y}}\hat{\mathrm{j}}-{\mathrm{v}}_{\mathrm{x}}\hat{\mathrm{i}}=-{\mathrm{v}}_{\mathrm{y}}\hat{\mathrm{j}}$

The velocity of bomb with respect to person sitting in plane is only in vertical direction. Thus, the trajectory of bomb with respect to the person will be a straight line vertically down to the plane.