anonymous
  • anonymous
how do i solve this Y = -16x^2 + 340x + 4500
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
Solve it for what? Do you mean you have to solve\[-16x^2+340x+4500=0\]?
anonymous
  • anonymous
Or do you have a particular x-value and you need to find y?
anonymous
  • anonymous
Or do you have a y-value and you need to find x?

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anonymous
  • anonymous
5200
anonymous
  • anonymous
Are you saying y=5200?
anonymous
  • anonymous
here is the whole problem
anonymous
  • anonymous
Well, it seems reasonable that y=5200 and you need to find the x-values that make it so.
anonymous
  • anonymous
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.
anonymous
  • anonymous
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
anonymous
  • anonymous
c. When, on the way up, might the projectile intersect the Red Baron
anonymous
  • anonymous
d. If the projectile misses the Red Baron on the way up, when might it intersect him on the way down?
anonymous
  • anonymous
Is the equation for y an equation you found or were you given that?
anonymous
  • anonymous
i found the equation
anonymous
  • anonymous
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?
anonymous
  • anonymous
yes it does
anonymous
  • anonymous
Your equation is correct...so now to finish...
anonymous
  • anonymous
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:\[5200=-16t^2+340t+4500\]
anonymous
  • anonymous
oh okay
anonymous
  • anonymous
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.
anonymous
  • anonymous
So there are you answers for c and d.
anonymous
  • anonymous
okay so how do i find out the two times it crosses the red barons path
anonymous
  • anonymous
\[t=\frac{5}{8}(17\pm \sqrt{177})\]
anonymous
  • anonymous
You solve the quadratic equation.
anonymous
  • anonymous
\[5200=-16t^2+340t+4500 \rightarrow -16t^2+340t-700=0\]
anonymous
  • anonymous
\[t = \frac{-340 \pm \sqrt{340^2-4(-16)(-700)}}{2(-16)}=\frac{-340 \pm \sqrt{70800}}{-32}s\]
anonymous
  • anonymous
using the quadratic formula (or you can complete the square).
anonymous
  • anonymous
\[\sqrt{70800}=20\sqrt{177}\]
anonymous
  • anonymous
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).
anonymous
  • anonymous
ok

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