### Specify the initial conditions...

p = .1    # x position of dog (0 <= p <= 1)
r = 40    # speed of dog

# ...and we'll do the rest!

t_e = sqrt(p^2+1)/r   # expected catch time

x = copy(p)
y = 1
t = 0
d = 0.0001

dogPoints = [(x,y)]

for i in [0..(1/d)]:
    x_1 = x + (r*d*(t-x)/(sqrt((t-x)^2+y^2)))
    y_1 = y + (r*d*(-y)/(sqrt((t-x)^2+y^2)))
    t = t + d

    dogPoints = dogPoints + [(x_1,y_1)]
    x = copy(x_1)
    y = copy(y_1)
    
    if sqrt(y^2+(x-t)^2) <= .001: 
        stop = x
        break

show(point(dogPoints) + plot(1, (x,0,1)) + point((t_e,0), color='red', marker="D"), xmin=0, xmax=1, ymin=0, ymax=1)
print "p=",p
print "r=",r
print "t_{expected}=",t_e
print "t_{computer}=",stop