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#import numpy package import numpy as np #define initial conditions #individual positions x0 = 0 #meters ##### Begin Editing ##### y0 = 100 # meters ##### End Editing ##### z0 = 0 #meters #position vector r0 = np.array([x0,y0,z0]) #indivitual velocities vx0 = 0 #m/s ##### Begin Editing ##### vy0 = -10 #m/s ##### End Editing ##### vz0 = 0 #m/s #velocity vector v0 = np.array([vx0,vy0,vz0])

t = 0 r = r0 y = r[1] deltat = 1 while t <= 11: #position update r = r + v0 * deltat #update time and position for conditional t += deltat y = r[1] if y <= 0: break print('Particle reached y={} after t={} seconds.'.format(y,t))

t = 0 r = r0 v = v0 y = r[1] g = 9.81 a = np.array([0,-g,0]) ##### Begin Editing ##### tc = np.sqrt(y) ##### End Editing ##### Ncycles = 10000 deltat = tc/Ncycles while t < 1.2 * tc: #position update r = r + v * deltat ##### Begin Editing ##### #Edit what's below to include the velocity update equation #velocity update v = v + a * deltat ##### End Editing ##### #update time and position for conditional t += deltat y = r[1] if y <= 0: break print('Particle reached y={} after t={} seconds.'.format(y,t))