Python

# solution starts below

# this line loads numpy and matplotlib - it has to be a part of your code

%pylab notebook

# Initialize Constants
V0 = 50
y0 = 1
x0 = 0
theta0 = 45*pi/180
Cd = .35
r = .23/(2*pi)
A = pi*r**2
m = .142

#Setting step size (dt) and number of points
n = 100
t = 8
dt = t/n

#Creating Arrays
x = zeros(n)
y = zeros(n)
vx = zeros(n)
vy = zeros(n)
theta = zeros(n)
v = zeros(n)

#Initializing conditions and finding trajectory
def trajectory(x, y, vx, vy, theta, v, g, D):
    x[1] = x0
    y[1] = y0
    theta[1] = theta0
    vx[1] = V0*cos(theta[1])
    vy[1] = V0*sin(theta[1])
    v[1] = V0
    for i in range(1, n-1):
        vx[i+1] = vx[i] - ((cos(theta[i])*.5*D*Cd*A*v[i]**2)/m)*dt #Change in vx due to horizontal component of air resistance
        vy[i+1] = vy[i] - ((sin(theta[i])*.5*D*Cd*A*v[i]**2)/m)*dt - g*dt #Change in vy due to vertical component of air resistance (and gravity)
        x[i+1] = x[i] + vx[i]*dt
        y[i+1] = y[i] + vy[i]*dt
        theta[i+1] = math.atan(vy[i+1]/vx[i+1])
        v[i+1] = sqrt(vx[i+1]**2+vy[i+1]**2)
        if(y[i+1] < 0):
            y[i+1] = 0
            vy[i+1] = 0

figure()
trajectory(x,y,vx,vy,theta,v,9.81,0)
plot(x,y,marker='o')
trajectory(x,y,vx,vy,theta,v,9.803,1.2)
plot(x,y,marker='o')
trajectory(x,y,vx,vy,theta,v,9.796,0.96)
plot(x,y,marker='o')
grid()
xlabel('Horizontal Displacement')
ylabel('Vertical Displacement')