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Thread: projectile

  1. #1
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    projectile

    A particle is projected at initial speed u from the top of a cliff of height h, the trajectory being out to sea in a plane perpendicular to the cliff.
    The particle strikes the sea at a distance d from the foot of the cliff.
    (i) Show that the possible times of flight can be obtained from the equation

    g2t4 4(u2 + gh)t2 + 4(h2 + d2) = 0.
    (ii) Hence or otherwise, prove that the maximum value of d for a particular u and h is
    im stuck on both parts.
    i started this off by using s=ut+.5at^2 take the projected point as the origin -h=0(t)+.5(-g)(t)^2 as the initial speed in the y direction is zero as its projected horizontally and when it hits the bottom its traveled -h in the y direction. this gets me t= √(2h/g)
    i have no idea idea about the equation

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  2. #2
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    Re: projectile

    Quote Originally Posted by markosheehan View Post
    A particle is projected at initial speed u from the top of a cliff of height h, the trajectory being out to sea in a plane perpendicular to the cliff.
    The particle strikes the sea at a distance d from the foot of the cliff.
    (i) Show that the possible times of flight can be obtained from the equation

    g2t4 – 4(u2 + gh)t2 + 4(h2 + d2) = 0.
    (ii) Hence or otherwise, prove that the maximum value of d for a particular u and h is
    im stuck on both parts.
    i started this off by using s=ut+.5at^2 take the projected point as the origin -h=0(t)+.5(-g)(t)^2 as the initial speed in the y direction is zero as its projected horizontally and when it hits the bottom its traveled -h in the y direction. this gets me t=[FONT="] √(2h/g)
    i have no idea idea about the equation [/FONT]
    How did you get that? That is what you should get if u= 0.

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  3. #3
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    Re: projectile

    the initial speed in the y direction is 0 i take it no?

    "the trajectory being out to sea in a plane perpendicular to the cliff." does this not mean its projected horizontally?

    ive tried putting the formula given in the question into the -b formula but i do not get any where with it.
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