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Math Help - projectile help

  1. #1
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    projectile help

    Hi, a projectile is fired with an initial speed of 500 m/s and angle of elevation 30 degrees.
    Find the range of the projectile, the max height, and speed at impact

    Thanks.
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  2. #2
    Newbie Arch_Stanton's Avatar
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    Firstly, we need to compute the component velocities.
    v_y=v_0 sin \alpha
    v_x=v_0 cos \alpha
    and duration of this movement:
    v_y=gt \Rightarrow t=\frac{v_y}{g}
    Maximum height is: h=\frac{gt^2}{2}=\frac{v_y^2}{2g}=\frac{v_0^2sin^2  \alpha}{2g}
    The rage: x=v_xt=v_0cos\alpha \frac{v_0sin \alpha}{g}=\frac{v_0^2sin \alpha cos\alpha}{g}
    The speed at impact is equal the initial speed.
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  3. #3
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    hmm

    what am I doing wrong w/ the range?
    I'm getting a 11km rather than 22km(book)
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  4. #4
    MHF Contributor
    skeeter's Avatar
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    because the correct range equation is ...

    \frac{2v_0^2 \cdot \sin{\theta}\cos{\theta}}{g} = \frac{v_0^2 \cdot \sin(2\theta)}{g}
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  5. #5
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    thank you

    !
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