A bomb is dropped from a plane travelling horizontally with uniform speed. Determine the location of the bomb relative to the plane at the time of explosion, and state whether this conclusion is true if the plane travels with uniform speed

Question

A bomb is dropped from a plane travelling horizontally with uniform speed. Determine the location of the bomb relative to the plane at the time of explosion, and state whether this conclusion is true if the plane travels with uniform speed but not horizontally.

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Correct answer: C. Vertically below the plane; the conclusion is true.

Let the velocity of the plane be v = v_x i + v_y 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 - 1 2 g t^2

A bomb is dropped from a plane travelling horizontally with uniform speed. Determine the location of the bomb relative to the plane at the time of explosion, and state whether this conclusion is true if the plane travels with uniform speed but not horizontally.

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