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Motion in A Plane question

2021 · 26 Aug · Shift 2 · Q56
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  5. /2021 · 26 Aug · Shift 2 · Q56

Motion in A Plane question

2021 · 26 Aug · Shift 2 · Q56

JEE MainPhysicsMotion in A PlaneMCQ+4 / −1
A bomb is dropped by fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a :
  1. A
    hyperbola
  2. B
    parabola in the direction of motion of plane
  3. C
    straight line vertically down the plane
  4. D
    parabola in a direction opposite to the motion of plane
View written solutionFree

Correct answer: C

  1. Choose the frame of reference

    The observer is sitting in the plane, so we analyze the bomb’s motion relative to the plane.

  2. Initial horizontal velocity of the bomb

    At the instant the bomb is dropped, it has the same horizontal velocity as the plane.

    Let the plane’s horizontal velocity be uuu.

    Then initially:

    • plane velocity =u= u=u horizontally
    • bomb velocity =u= u=u horizontally

  3. Relative horizontal motion

    Since both plane and bomb have the same horizontal velocity at release, the bomb’s horizontal velocity relative to the plane is

    u−u=0u-u=0u−u=0

    Also, if the plane continues flying with constant velocity, its horizontal acceleration is zero, while the bomb also has no horizontal acceleration (neglecting air resistance).

    So the bomb has no relative horizontal motion with respect to the plane.

  4. Relative vertical motion

    Vertically, the bomb starts with zero relative velocity and then accelerates downward due to gravity:

    y=12gt2y = \frac{1}{2}gt^2y=21​gt2

    downward relative to the plane.

  5. Shape of trajectory as seen from the plane

    Since there is no relative horizontal displacement and only vertical downward displacement, the bomb appears to move along a

    straight vertical line downward.

  6. Check options

    • A: hyperbola — incorrect
    • B: parabola in the direction of motion of plane — incorrect
    • C: straight line vertically down the plane — correct
    • D: parabola in a direction opposite to the motion of plane — incorrect

Therefore, the correct answer is C.

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