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).

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)

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

To find the time when the projectile intersects the Red Baron, we need to find the common time at which both Snoopy's projectile and the Red Baron's altitude are the same.

Let's consider the upward motion of the projectile. The equation that describes the height of the projectile at any given time can be derived using the kinematic equation for motion with constant acceleration:

y = y0 + v0t + (1/2)at^2

Where:
y is the height of the projectile (altitude)
y0 is the initial height of the projectile (4500 ft)
v0 is the initial velocity of the projectile (340 ft/s)
t is the time after firing in seconds

Since the projectile is moving upward, the acceleration is negative, due to gravity. So, a = -32 ft/s^2 (acceleration due to gravity).

Therefore, the equation to describe the upward motion of the projectile is:

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

Now, the Red Baron maintains a constant altitude of 5200 ft. To find the common time when the projectile intersects the Red Baron, we need to equate the height of the projectile (y) to the Red Baron's altitude (5200 ft):

4500 + 340t - (16t^2) = 5200

To solve this equation, we bring all the terms to one side:

16t^2 - 340t + 700 = 0

Now we can solve this quadratic equation to find the values of t when the projectile intersects the Red Baron. Use the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

Where:
a = 16
b = -340
c = 700

Plugging in these values, we get:

t = (-(-340) ± √((-340)^2 - 4(16)(700))) / (2(16))
t = (340 ± √(115600 - 44800)) / 32
t = (340 ± √(70800)) / 32

Calculating the square root and simplifying, we have:

t ≈ 0.2812 seconds or t ≈ 21.969 seconds

So, there are two possible times when the projectile might intersect the Red Baron: approximately 0.2812 seconds after firing and approximately 21.969 seconds after firing.