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0. A bomb is dropped from a plane flying horizontally with uniform speed. Show that the bomb will explode vertically below the plane. Is the statement true if the plane flies with uniform speed but not horizontally  ?  

Answer: When the plane flying horizontally with a uniform speed, say u, drops a bomb, it gives a uniform horizontal speed u also to the bomb. So the bomb will move horizontally just below the plane but their vertical separation will increase with the time. If it explodes in the air, the bomb will be vertically below the plane. See the diagram below.

       If the plane flies with an angle θ with the horizontal with uniform speed u , both the plane and the bomb will have same speed and direction at the time of dropping the bomb. Both the plane and the bomb will have horizontal component of speed equal to 'u cosθ'  and  vertical component of speed equal to 'u sinθ' at the time of separation. The vertical component of speed 'u sinθ' for the plane remains constant but for the bomb varies according to uniform accelerated motion under the gravity. So their vertical separation varies with time. But the horizontal component of the speed 'u cosθ' remains the same, so both the plane and the bomb move with same speed horizontally and even in this case the bomb will explode vertically below the plane. Hence the statement is still true. See the diagram below.