#y = 100-10t
#when y=0, t=10
#import numpy package
import numpy as np
#define initial conditions
#individual positions
x0 = 0 #meters
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y0 = 100 # meters
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z0 = 0 #meters
#position vector
r0 = np.array([x0,y0,z0])
#indivitual velocities
vx0 = 0 #m/s
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vy0 = -10 #m/s
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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])
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tc = np.sqrt(y/g)
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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))