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anonymous

  • 5 years ago

how do i solve this Y = -16x^2 + 340x + 4500

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  1. anonymous
    • 5 years ago
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    Solve it for what? Do you mean you have to solve\[-16x^2+340x+4500=0\]?

  2. anonymous
    • 5 years ago
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    Or do you have a particular x-value and you need to find y?

  3. anonymous
    • 5 years ago
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    Or do you have a y-value and you need to find x?

  4. anonymous
    • 5 years ago
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    5200

  5. anonymous
    • 5 years ago
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    Are you saying y=5200?

  6. anonymous
    • 5 years ago
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    here is the whole problem

  7. anonymous
    • 5 years ago
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    Well, it seems reasonable that y=5200 and you need to find the x-values that make it so.

  8. anonymous
    • 5 years ago
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    2) Snoopy is in his plane, 4500 feet above the ground. He fires a projectile straight up. The initial velocity of the projectile is 340 feet per second. (After the projectile is fired, it has no acceleration, so its height can be modeled by a “falling body” model.) The Red Baron is maintaining a constant altitude of 5200 feet.

  9. anonymous
    • 5 years ago
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    a. Write an equation describing the upward motion of the projectile. (Assume there is no air resistance. Let y represent the altitude of the projectile in feet, and let t represent the time after firing in seconds.) • Y = -16x^2 + 340x + 4500

  10. anonymous
    • 5 years ago
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    c. When, on the way up, might the projectile intersect the Red Baron

  11. anonymous
    • 5 years ago
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    d. If the projectile misses the Red Baron on the way up, when might it intersect him on the way down?

  12. anonymous
    • 5 years ago
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    Is the equation for y an equation you found or were you given that?

  13. anonymous
    • 5 years ago
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    i found the equation

  14. anonymous
    • 5 years ago
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    Well, the problem will depend on the coordinate system you use. If you 'attach' a coordinate system to Snoopy, then when he fires the projectile straight up, it will look like (in your coordinate system) the object is being fired straight up the y-axis. I'm assuming the Red Barron is directly above Snoopy and travelling with same velocity. Does this agree with you so far?

  15. anonymous
    • 5 years ago
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    yes it does

  16. anonymous
    • 5 years ago
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    Your equation is correct...so now to finish...

  17. anonymous
    • 5 years ago
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    y will be 5200, since your coordinate system is based on the ground, though moving along with Snoopy, so you have to solve for t in:\[5200=-16t^2+340t+4500\]

  18. anonymous
    • 5 years ago
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    oh okay

  19. anonymous
    • 5 years ago
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    There will be two times: the first is the initial impact, the second when it comes back down. It has the same momentum in the x-direction as Snoopy and the Red Barron.

  20. anonymous
    • 5 years ago
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    So there are you answers for c and d.

  21. anonymous
    • 5 years ago
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    okay so how do i find out the two times it crosses the red barons path

  22. anonymous
    • 5 years ago
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    \[t=\frac{5}{8}(17\pm \sqrt{177})\]

  23. anonymous
    • 5 years ago
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    You solve the quadratic equation.

  24. anonymous
    • 5 years ago
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    \[5200=-16t^2+340t+4500 \rightarrow -16t^2+340t-700=0\]

  25. anonymous
    • 5 years ago
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    \[t = \frac{-340 \pm \sqrt{340^2-4(-16)(-700)}}{2(-16)}=\frac{-340 \pm \sqrt{70800}}{-32}s\]

  26. anonymous
    • 5 years ago
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    using the quadratic formula (or you can complete the square).

  27. anonymous
    • 5 years ago
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    \[\sqrt{70800}=20\sqrt{177}\]

  28. anonymous
    • 5 years ago
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    Then just simplify to get the answers above. The lower time will be the first strike (answer c), the larger time will be the second strike (answer d).

  29. anonymous
    • 5 years ago
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    ok

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