Description
Lists and More Turtles:
1. (a) Create a program staRect.py. The program takes two integers, R and C,
as inputs and prints an R C rectangle array of asterisks (*). For example,
R = 5, C = 10 should produce:
Note: When you use print(“A”) it adds a newline character (‘‘\n’’).
To avoid the newline character, use print(“A”, end=‘‘’’)
(b) Modify staRect.py to accept a single integer R as input and produce a
triangle with a single star in the first row, two in the second, etc. Save the
program as sTri.py.
2. In this exercise, we explore projectile motion, using the turtle module.
Consider the motion of a projectile, launched at a velocity v0 at an angle θ
to the horizontal (x-axis). The simplest approximation to the motion of the
projectile is when the only force acting on the projectile is its own weight: mg
where g is the acceleration due to gravity (9.81m/s2
). Using the equations of
motion (v(t) – velocity; s – displacement, t – time):
v = v0 − g ∗ t (1)
s = s0 + v0 ∗ t −
1
2
g ∗ t
2
(2)
The motion of the projectile can be broken down into two independent components of the motion:
1
(i) Along the x-axis, with an acceleration ax = 0 and an initial velocity v0x =
v0 ∗ cos θ and (ii) Along the y-axis, with an acceleration ay = −g (the negative
sign indicates that it is pointing downwards.) and the initial velocity: v0y ∗ sin θ
Along the horizontal and vertical directions:
vx = v0 ∗ cos θ and x = x0 + v0 ∗ cos θ ∗ t. (3)
vy = v0 ∗ sin θ − g ∗ t and y = y0 + v0 ∗ sin θ ∗ t −
1
2
g ∗ t
2
(4)
Using the x and y equations above, plot the trajectory of a turtle launched at an
angle θ, and initial velocity v0 (entered by the user). To compute cos, sin etc.
import math, convert the angle entered in degrees, θ, into radians (θ ∗ π/180).
Use as: math.cos(θ∗π/180). The math module expects angles in radians). Fire
the projectile from (x0, y0) = (−200, 0).
• Pick a travel time that will (at least) cover the entire range of the x
motion (experiment to find the right travel time).
• Compute the (x, y) position at small time increments (using the x and y
equations above) making up the total travel time. A convenient way to
do this is to use the range function in the form: range(start, stop,
step). The step parameter allows you to control the increment (the default increment is 1).
(See: https://docs.python.org/3/library/functions.html#func-range).
Use the turtle stamp() function to leave an impression of the turtle at
each time-increment.
• Create lists for x, y and time and append each new x, y and time value
to the respective lists. Print the lists (side-by-side) after the turtle has
finished moving.
• Modify your program to compute an estimate of and print the max. distance the turtle travels in the x-direction (the “range”). The range is found
by finding the time at which the y position of the turtle first becomes ≤ 0,
and then using that time in the x equation.
• Modify your program to find the maximum height the projectile reaches.
When the projectile is at its maximum height, vy = 0. You can approximate
this using the vy equation: Find the time when vy switches from positive
to negative. Use the time in the y equation to find the max. height.
2
• Finally, save a copy of your program and change it to create a list of firing
angles θ from 20 to 80 degrees, in steps of 5 degrees (with fixed value for
v0) and make a list of the max. heights reached and a list of the max.
x-value (range) reached, for each value in the list of firing angles.
Below is the turtle trajectory for x0 = −200, y0 = 0, θ = 60, v0 = 70m/s
3 CSCI 2202 Lab 3 Lists
