""""Exercise 2.8 from "A Primer on ..." 
Generate a nicely formatted table of t and y values, 
The t values should be n + 1 equally spaced t 
values on the interval [a,b], and the y values are
computed with the given formula. 
"""

#a) Using a for-loop
v0 = 5
g = 9.81
n = 5

a = 0
b = 2 * v0 / g
h = (b - a) / n

for i in range(n + 1):
    t = a + h * i
    y = v0 * t - 0.5 * g * t**2
    print(f"{t:5.5f} {y:5.5f}")

t = a

print("#####")


#b) Same task using a while-loop
eps = 1e-10

while t < b + eps: #safer than using t<=b, because of roundoff error
    y = v0 * t - 0.5 * g * t**2
    print(f"{t:5.5f} {y:5.5f}")
    t = t + h


"""
Terminal> python ball_table1.py 
0.00000 0.00000
0.20387 0.81549
0.40775 1.22324
0.61162 1.22324
0.81549 0.81549
1.01937 0.00000
#####
0.00000 0.00000
0.20387 0.81549
0.40775 1.22324
0.61162 1.22324
0.81549 0.81549
1.01937 0.00000
"""