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**1. Homework Statement**

I was at the firing range the other day when the gun instructor mentioned that the bullet of a AR-15 rifle can travel 5 - 6 miles depending on the angle of the gun when the bullet leaves the muzzle. I wanted to confirm this for myself so, I tried to find the range by plugging in all the known values to the parabolic trajectory equation.

Neglecting air drag and taking only gravity into account, how far does the bullet travel? Here are the know values:

Muzzle Velocity = 975m/s

Height of gun = 1.7m

θ = 45°

**2. Homework Equations**

y = (Tan θ)x

_{o}- (g/(2v

^{2}

_{o}Cos

^{2}θ))x

^{2}

y = Height of gun [m]. This is -1.7m in this instance

v

_{o}= Initial velocity/muzzle velocity [m/s]

x = unknown distance [m]

**3. The Attempt at a Solution**

When I plug all the values into the equation, I get the quadratic equation:

0 = 1.7+1x-.00001x

^{2}

Solving the equation gives me x = -1.69997 and x = 100,002m

This is clearly over 5 - 6 miles. This is about 61 miles. I tried this several times, and I am stumped. My questions are:

- Should I use another formula?
- Does ignoring air drag cause the discrepancy in the calculations?

If someone can steer me in the right direction, I can do the calculations myself. Any help would be appreciated.

Thanks!