Question

Engr 135 Program #6 Spring 2019 Cannon Muzzle Velocity& Projectile Impact Point Part I- Cannon Muzzle Velocity We wish to determine the muzzle velocity of a physics lab spring "cannon." The cannon will be fired from a table top, with the cannon itself parallel to the floor. It is established that the height of the bottom of the ball, just as it is leaving the cannon, is Yo in meters. We assume that for the short distances and velocities involved, is that air friction on the projectile is negligible. The first part of your program is to query your program user for the height of the projectile, Yo, in meters, and the impact point of the projectile, Xf, in meters You will then calculate the flight time for the projectile's flight, tf, in seconds, and You will output Yo, Xf, and Vmuzzle, with appropriate units, to the command obtained from the experimental firing of the cannon. the effective average muzzle velocity, Vo -Vmuzzle in meters/second. window Part II Impast Point Prediction when Shooting Cannon at an Augle to Horizontal The cannon is now set an angle to the horizontal, and it is likely that Yo has changed. We wish to predict the new impact point Xf, in meters, when firing the cannon with the same ball. It is assumed that the muzzle velocity of the cannon, Vmuzzle, is the same as the muzzle velocity established in Part I . Query yo ur program user for the height of the projectile, Yo, in meters, and the angle theta, in degrees with which the cannon is being fired. . You will then calculate the flight time for the projectile's flight, tf, in seconds, and the downrange inpact point Xf, in meters, at which the projection first touches the ground You will then output Yo、theta, and Xf, with appropriate units, to the command window. ·

Answer 1

THE CODE FOR THE ABOVE QUESTION IS :

# standard acceleration of gravity in meters per second square
from math import sqrt, sin, cos, radians

# declaring our global variables
g = 9.80
Vmuzzle = 0


def part_I():
    global g, Vmuzzle
    Y0 = float(input('Enter the height of the projectile in meters: '))
    Xf = float(input('Enter the impact point of the projectile in meters: '))

    # calculating time taken to hit the ground
    # S = Uy.t + (1/2).g.t^2
    # Uy is 0 initially
    # so t = square_root (2*S/g)
    t = sqrt(2 * Y0 / g)

    # velocity is distance / time
    Vmuzzle = Xf / t

    print('Height of projectile:', Y0, 'meters')
    print('Impact point of projectile:', Xf, 'meters')
    print('Average muzzle velocity of projectile:', round(Vmuzzle, 2), 'meters per second')


def part_II():
    global g, Vmuzzle
    Y0 = float(input('Enter the height of the projectile in meters: '))
    theta = float(input('Enter the angle of the projectile in degrees: '))

    # Vertical component of velocity Vy = Vmuzzle.sin(theta)
    # Horizontal component of velocity Vx = Vmuzzle.cos(theta)
    Vy = Vmuzzle * sin(radians(theta))
    Vx = Vmuzzle * cos(radians(theta))

    # total flight time = time it goes up + time it takes to come down
    # time it goes up = 2 * (Vy / g)
    t_up = 2 * (Vy / g)

    # time it takes to come down can be found by solving for time in the equation
    # (1/2).g.t^2 + Vy.t - S = 0
    # we will discard this root as time is never negative
    # t2 = -Vy/g - sqrt(Vy**2 + 2*Y0*g)/g
    t_down = -Vy / g + sqrt(Vy ** 2 + 2 * Y0 * g) / g

    t_total = t_up + t_down
    Xf = Vx * t_total

    print('Height of projectile:', Y0, 'meters')
    print('Angle of projectile:', theta, 'degrees')
    print('Downrange impact point of projectile:', round(Xf, 2), 'meters')


if __name__ == '__main__':
    part_I()
    print()
    part_II()

Screenshot of the code:

# standard acceleration of gravity in meters per second square from math import sqrt, sin, cos, radians # declaring our global variables g 9.80 Vmuzzle0 def part_I): 10 global g, Vmuzzle Y0 = float (input ('Enter the height of the projectile in meters: ')) XE = float (input ('Enter the impact point of the projectile in meters: ')) 12 13 14 15 16 17 18 # calculating time taken to hit the ground # uy is o initially # so t = square-root (2*S/g) t = sqrt (2 * Y0 / g) 20 # velocity is distance / time Vmuzzle Xf / t 21 print ('Height of projectile:', ro, 'meters) print ('Impact point of projectile:",xf, 'meters') print ('Average muzzle velocity of projectile:', round (Vmuzzle, 2) 'meters per second') 23 24 25 26 27 28 29 30 3I 32 def part IIO global g, Vmuzzle YO = float (input ('Enter the height of the projectile in meters: ')) theta = float (input ('Enter the angle of the projectile in degrees: ')) # vertical component of velocity vy vmuzzle.sin (theta) # Horizontal component of velocity vx = v muzzle.cos (theta) Vy = Vmu z złe * sin(radians (theta)) Vx Vmuzzle cos (radians (theta)) 34 35 36 37 38 39 # total flight time time it goes up + time it takes to come down #time it goes up # 2 * (Vy / g) t-up = 2 * (Vy / g)


42 43 # time it takes to come down can be found by solving for time in the equation we will discard this root as time is never negative t_down -Vy/g+ sqrt (Vy 2+2YOg)lg ttotal = tup + t down 45 수 47 48 49 50 E = vx * t total print ('Height of projectile:', Yo, 'meters' print ('Angle of projectile:', theta, 'degrees') print ('Downrange impact point of projectile:', round (Xf, 2), 'meters') 51 52 54 if name main: 58 59 60 part I(O print () part II ()


SAMPLE OUTPUT :

Enter the height of the projectile in meters: 60 Enter the impact point of the projectile in meters: 87 Height of projectile: 60.0 meters Impact point of projectile: 87.0 meters Average muzzle velocity of projectile: 24.86 meters per second Enter the height of the projectile in meters: 60 Enter the angle of the projectile in degrees: 5:3 Height of projectile: 60.0 meters Angle of projectile: 53.0 degrees Downrange impact point of projectile: 90.82 meters 2 2