# Applying Algebraic Thinking to Data

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Snoopy is in his plane, 4500 ft above ground. he fires a projectile straight up. The Vo of the projectile is 340 ft/s. (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 5200ft.
1. Write an equation describing the upward motion of the projectile.
***No air resistance.
***Let y represent altitude of the projectile (feet).
***let t represent time after firing in sec.
~~ 5200=-16t^2+340t+4500~~ IS THAT EQUATION CORRECT?
2. When, on the way up, might the projectile intersect the Red Baron? (THIS IS WHERE IM STUCK).

• Applying Algebraic Thinking to Data -

since we have no idea of the speed of the planes, we can only assume yu need to find when the height of the projectile is 5200 ft. Then ,if Snoopy is extremely lucky, he just might hit the Red Baron.

So, since your equation is correct, just solve

y = -16t^2+340t+4500

when y = 5200, as you showed above.
What's the problem? It's just a simple quadratic.

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

t = 5/8 (17 ± √177)

• Applying Algebraic Thinking to Data -

at t = 5/8 (17 - √177) the missile is going up
at t = t = 5/8 (17 + √177) it is coming back down.

To see this, go to wolframalpha . com and type in

solve 5200=-16t^2+340t+4500

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