""""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. 
"""

#values for v0, g and n:
v0 = 5
g = 9.81
n = 5

#compute the boundaries a and b, and the distance between points, h:
a = 0
b = 2 * v0 / g
h = (b - a) / n


#a) using a for loop
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}')

print('######')

#b)
t = a
eps = 1e-10

i = 0
while  t < b + eps:
    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
"""

"""
Comment on the solution:
The recipe for generating the t values is exactly the same as in 
Ex 2.7 (coor.py). There are two main points to this exercise:
1. Using an f-string to print the output as a "nicely formatted table"
2. Getting the limit right in the while loop. Because of roundoff
error a condition like t <= b may give inconsistent results. It usually works, 
but sometimes it fails because the numbers are supposed to be equal, but roundoff error
makes t > b. The solution is to introduce a small tolerance (here called eps) and
formulate the condition as in the code. 
"""