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18 March, 10:17

During World War I, the Germans had a gun called Big Bertha that was used to shell Paris. The shell had an initial speed of 1.4 km/s at an initial inclination of 65.8 ◦ to the horizontal. The acceleration of gravity is 9.8 m/s 2. How far away did the shell hit?

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  1. 18 March, 10:48
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    The shell hit at a horizontal distance 149.41 km

    Explanation:

    The shell had an initial speed of 1.4 km/s

    Initial speed = 1400 m/s

    Inclination = 65.8° to the horizontal

    First let us find the time of travel

    Consider the vertical motion,

    We have equation of motion, s = ut + 0.5 at²

    Initial velocity, u = 1400 sin 65.8 = 1276.97 m/s

    Acceleration, a = - 9.81 m/s²

    Displacement, s = 0 m

    Substituting

    s = ut + 0.5 at²

    0 = 1276.97 x t + 0.5 x (-9.81) xt²

    t = 260.34 s

    Now let us find the horizontal displacement,

    Consider the horizontal motion,

    We have equation of motion, s = ut + 0.5 at²

    Initial velocity, u = 1400 cos 65.8 = 573.89 m/s

    Acceleration, a = 0 m/s²

    Time, t = 260.34 s

    Substituting

    s = ut + 0.5 at²

    s = 573.89 x 260.34 + 0.5 x 0 x 260.34²

    s = 149407.11 m = 149.41 km

    The shell hit at a horizontal distance 149.41 km
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