## anonymous 5 years ago how do i solve this Y = -16x^2 + 340x + 4500

1. anonymous

Solve it for what? Do you mean you have to solve$-16x^2+340x+4500=0$?

2. anonymous

Or do you have a particular x-value and you need to find y?

3. anonymous

Or do you have a y-value and you need to find x?

4. anonymous

5200

5. anonymous

Are you saying y=5200?

6. anonymous

here is the whole problem

7. anonymous

Well, it seems reasonable that y=5200 and you need to find the x-values that make it so.

8. 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.

9. 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

10. anonymous

c. When, on the way up, might the projectile intersect the Red Baron

11. anonymous

d. If the projectile misses the Red Baron on the way up, when might it intersect him on the way down?

12. anonymous

Is the equation for y an equation you found or were you given that?

13. anonymous

i found the equation

14. 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?

15. anonymous

yes it does

16. anonymous

Your equation is correct...so now to finish...

17. 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:$5200=-16t^2+340t+4500$

18. anonymous

oh okay

19. 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.

20. anonymous

So there are you answers for c and d.

21. anonymous

okay so how do i find out the two times it crosses the red barons path

22. anonymous

$t=\frac{5}{8}(17\pm \sqrt{177})$

23. anonymous

24. anonymous

$5200=-16t^2+340t+4500 \rightarrow -16t^2+340t-700=0$

25. anonymous

$t = \frac{-340 \pm \sqrt{340^2-4(-16)(-700)}}{2(-16)}=\frac{-340 \pm \sqrt{70800}}{-32}s$

26. anonymous

using the quadratic formula (or you can complete the square).

27. anonymous

$\sqrt{70800}=20\sqrt{177}$

28. 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).

29. anonymous

ok