projectile_trajectory.rb

require 'mathn'

# Just a class with methods for calculating trajectories of a projectile
# Read more: http://en.wikipedia.org/wiki/Trajectory_of_a_projectile
class ProjectileTrajectory
  attr_accessor :grav_acceleration, :launch_angle, :launch_velocity,
    :initial_height, :distance_traveled

  def initialize(g=9.81, theta, v, y_not)
    self.grav_acceleration = g     # the gravitational acceleration (usually taken to be 9.81 m/s^2 near the Earth's surface)
    self.launch_angle      = theta # the angle at which the projectile is launched (in degrees)
    self.launch_velocity   = v     # the velocity at which the projectile is launched
    self.initial_height    = y_not # the initial height of the projectile
  end

  def distance_traveled
    if initial_height.to_i == 0 && launch_angle.to_i == 45
      distance_traveled = ((launch_velocity**2) / grav_acceleration)
    elsif initial_height.to_i == 0
      distance_traveled = ((launch_velocity**2) * Math.sin(2*launch_angle)) / grav_acceleration
    else
      distance_traveled = ((launch_velocity*Math.cos(launch_angle) / grav_acceleration) * ((launch_velocity*Math.sin(launch_angle)) + Math.sqrt((launch_velocity*Math.sin(launch_angle))**2 + (2*grav_acceleration*initial_height))))
    end
  end

  def flight_time
    distance_traveled / (launch_velocity * Math.cos(launch_angle))
  end

  # the angle at which a projectile must be launched
  # in order to reach a desired distance, given the launch_velocity
  def angle_of_reach(desired_distance)
    0.5 * Math.asin((grav_acceleration*desired_distance) / (launch_velocity**2))
  end

  # the height of the projectile given a horizontal_distance
  def height(horizontal_distance)
    initial_height + (horizontal_distance * Math.tan(launch_angle)) - ((grav_acceleration * (horizontal_distance**2)) / (2*((launch_velocity*Math.cos(launch_angle))**2)))
  end

  # the velocity of the projectile given a horizontal_distance
  def velocity(horizontal_distance)
    Math.sqrt((launch_velocity**2) - (2*grav_acceleration*horizontal_distance*Math.tan(launch_angle)) + ((grav_acceleration*horizontal_distance) / (launch_velocity*Math.cos(launch_angle))))
  end

  # Angle required to hit a target at range x and altitude y when
  # fired from (0,0) and with launch_velocity
  def angle_required_to_hit_coordinate(x,y)
    numerator = (launch_velocity**2) + Math.sqrt((launch_velocity**4) - (grav_acceleration*(grav_acceleration*(x**2)) + 2*y*(launch_velocity**2)))
    Math.atan(numerator / (grav_acceleration * x))
  end
end