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Math Help - Projectile problem

  1. #1
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    Projectile problem

    Hi - I'm needing help with this one - cannot quite get it. Thanks

    An airplane in level flight at an altitude of 7000 m is moving at 500 m/s. At the moment it flies overhead, a ground missile is fired at a constant acceleration of 80 m/s/s. What aiming angle above the ground must be used to hit the airplane?
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  2. #2
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    Quote Originally Posted by Lucymathgirl View Post
    Hi - I'm needing help with this one - cannot quite get it. Thanks

    An airplane in level flight at an altitude of 7000 m is moving at 500 m/s. At the moment it flies overhead, a ground missile is fired at a constant acceleration of 80 m/s/s. What aiming angle above the ground must be used to hit the airplane?
    let \theta be the launch angle above the horizontal

    a_x = 80\cos{\theta}

    a_y = 80\sin{\theta}

    since acceleration is constant and initial velocity = 0 ...

    \Delta x = 500t = \frac{1}{2}a_x t^2

    \Delta y = 7000 = \frac{1}{2}a_y t^2

    solve the system for t and \theta
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  3. #3
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    mathing it out

    Thanks - working it through, then, I can get for the horizontal that t=cos theta/12.5, and for the vertical that t squared = 175/sin theta. This is where I get stuck.
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  4. #4
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    Quote Originally Posted by Lucymathgirl View Post
    Thanks - working it through, then, I can get for the horizontal that t=cos theta/12.5, and for the vertical that t squared = 175/sin theta. This is where I get stuck.
    correction ... t = \frac{12.5}{\cos{\theta}}
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  5. #5
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    oh right, thank you, so now how do i solve for t or theta?
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  6. #6
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    substitute the corrected expression for t in the \Delta y equation, then solve for \theta.
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  7. #7
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    are trig. identities required to solve for sin theta?
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  8. #8
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    Quote Originally Posted by Lucymathgirl View Post
    are trig. identities required to solve for sin theta?
    It seems from your responses that you are not confident in using your algebra and trig skills.

    If such is the case, then I recommend you solve the equation using your calculator. If your calculator skills are wanting, then I advise that you have a face-to-face session with your instructor.
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  9. #9
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    Thanks

    Hi - yes, I am just learning this area of trig, but I think that I have it solved now. Thanks so much for your help!
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