# This lab session is to get them used to the editor, running python scripts
# and using python as a calculator. Since I want them to get used to the
# editor, they should be discouraged from using the python interpreter, even
# though that is easier to use.

# Make all of them open an editor. Give them some problem whose solution
# just uses formulas involving +, -, * , / and ** (raising to the power).
# Here are some examples.

# 1. Two trains T and R are moving on the x-axis with velocities 12 m/s and
# 11.5 m/s respectively. Suppose at time t = 0 suppose they are at the
# points 0 and 1 respectively. At what time, will they collide? Where will
# the collide?
u = 12.0
v = 11.5
# pos_T_at_t = 0 + u * t
# pos_R_at_t = 1 + v * t
# We want to solve pos_T_at_t - pos_R_at_t = 0 for t. That is, -1 + (u - v)
# * t = 0. Therefore, t = 1 / (u - v)
t = 1 / (u - v)
pos = u * t
print "Prob 1 : The trains will collide in %g at time %g." % (pos, t)


# 2. Formula for compound interest. Suppose the principal is P, the interest
# rate be r/100 and the number of years by n. Then the total amount of n
# years is P(1 + r/100)^n.
P = 100
r = 5.0
n = 5
C = P * ( 1 + r / 100)**n
print "Prob 2 : Total sum after 5 years is %g." % C

# 3. Find the sum 1 + 2 + ... + 100 using the formula 1 + .. + n = n (n+1)
# /2
n = 100
S = n * (n + 1) / 2.0
print "Prob 3 : 1 + ... + 100 = %d." % S

# 4. Write all the above in an editor, save it as a .py file and email it to
# themselves?