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6 June, 21:36

The muzzle velocity of an armor-piercing round fired from an M1A1 tank is 1770 m/s (nearly 4000 mph or mach 5.2). A tank is at the top of a cliff and fires a shell horizontally. If the shell lands 6520 m from the base of the cliff, how high is the cliff?

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  1. 6 June, 21:54
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    Height of cliff is 66.43 meter.

    Explanation:

    Consider the horizontal motion of shell,

    We have equation of motion s = ut + 0.5 at²

    Initial velocity, u = 1770 m/s

    Acceleration, a = 0 m/s²

    Displacement, s = 6520 m

    Substituting

    s = ut + 0.5 at²

    6520 = 1770 x t + 0.5 x 0 xt²

    t = 3.68 s

    Time of flight of shell = 3.68 s.

    Now consider the vertical motion of shell,

    We have equation of motion s = ut + 0.5 at²

    Initial velocity, u = 0 m/s

    Acceleration, a = 9.81 m/s²

    Time, t = 3.68 s

    Substituting

    s = ut + 0.5 at²

    s = 0 x 3.68 + 0.5 x 9.81 x 3.68²

    s = 66.43 m

    Height of cliff is 66.43 meter.
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