1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Bullet trajectory; solving for required angle of elevation

  1. May 26, 2010 #1
    The problem statement, all variables and given/known data
    Bob is trying to hit a stationary target 146.00m downrange, his eyes are 1.8m above the ground, firing from a standing position. The muzzle velocity of the projectile is 382.524m/sec (1255 ft/sec), wind is negligible; at what firing angle must he fire to successfully hit the target? The target is 1m above the horizontal.

    DATA
    Variables
    T: projectile flight time in seconds
    V: projectile velocity (m/s)
    g: gravity in m/s^2
    a (theta): required firing angle in degrees

    Test/develop environment: Controlled
    Overview: Set up markers to a distance of 200m, 1 marker per 25m
    Program will not compensate for cross-winds, humidity, etc.

    Required information:
    1)Drag factor
    2)Launch angle
    3)Initial velocity
    4)Gravity (Default: 9,8022m/s^2)
    5)Shape of parabola

    Variables:
    T: Projectile flight time in seconds
    V: Projectile velocity in m/s
    g: gravity in m/s^2
    a: Required firing angle in degrees

    Test-caliber: Winchester Wildcat .22 High Velocity
    Point: Solid
    Bullet weight: 40 grains (2.59196 grams)
    Muzzle velocity (m/s): 382.524
    Velocity @ 100m: 1017 (18.96% decrease
    Muzzle energy (ft/lbs):139.82
    Energy @ 100m (ft/lbs):91.82 (34.33% decrease)
    Ballistic coefficient: .100

    Attempt at a solution:
    Would I use this formula to find the angle of elevation?

    "Angle θ required to hit coordinate (x,y)" @ http://en.wikipedia.org/wiki/Trajectory_of_a_projectile

    θ = tan-1((v2 +/- ((v4-g(gx2+2yv2)))0.5)/gx)

    The above formula does not compensate for air resistance, so should I scrap that formula and seek an alternative derivation?
     
    Last edited: May 26, 2010
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted