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Question
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?
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Solution
The plane is flying horizontally with a uniform speed. Therefore, the bomb also has the same speed.
Let the speed of the plane be represented by u.
Now, let t be the time taken by the bomb to reach the ground.
Distance travelled by the bomb in horizontal direction = ut
Both the plane and bomb are travelling in the same direction.
Distance travelled by the plane in the same time = ut
Hence, the bomb will explode vertically below the plane.
When the plane is flying with a uniform speed but not horizontally:
Let us consider it will make an angle of projection θ along the horizontal direction.
So, both the plane and the bomb will be flying with the same angle of projection.
Therefore, both will have the same horizontal speed u cos θ, where u is the initial speed of the plane and the bomb.
When the bomb is released, the time taken by the bomb to reach the ground is t.
The distance travelled by the bomb and the plane will be u cos θt.
Hence, again the bomb will explode vertically below the plane.
(i) During the motion of bomb, its horizontal velocity u remains constant and is the same as that of the plane at every point of its path.
Let the bomb reach the ground in time t.
Distance travelled in horizontal direction by the bomb = ut
Distance travelled in horizontal direction by the bomb is the same as that travelled by the plane.
So, the bomb will explode vertically below the plane.
(ii) Let the plane move making an angle α with the horizontal.
Horizontal distance for both the bomb and the plane = u cos αt'
t' = Time taken by the bomb to reach the ground
So, in this case also, the bomb will explode vertically below the plane.
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