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Math Help - Projectiles

  1. #1
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    Projectiles

    over level ground, the greatest range of a gun is 25km. the muzzle velocity of a bullet leaving the barrel of this gun is ?

    no idea where to start.
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  2. #2
    MHF Contributor Unknown008's Avatar
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    Well, the greatest range is achieved on level ground when a projectile is fired at an angle of 45 degrees with the horizontal.

    I don't know if you're supposed to know the range formula,. So, I'll use the long way.

    Let the muzzle velocity be v.

    Along the horizontal, you have a component v \cos(45)

    Along the vertical, you have a component v \sin(45)

    The time for the projectile to land is obtained using the vertical component:

    s = ut + \dfrac12 at^2

    s = 0,
    u = v cos(45)
    t = ?
    a = -9.8

    From this, you get an equation with v and t.

    The next part is when taking the horizontal component.

    In time t, it covers distance d.

    d = ut

    d = 25 km = 25000 m
    u = v sin(45)
    t = ?

    This gives you another equation with v and t.

    Solve simultaneously to get the value of v.
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  3. #3
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    you answered me in your very first line.
    i didn't know it was 45 degrees.
    I am so sorry you have to type that all out.
    But Thank you ever so much.!
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  4. #4
    MHF Contributor Unknown008's Avatar
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    It's okay
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