ENGG1001: Programming for Engineers
> Assignment 1 (10 Marks)
Due: Friday 26th March, 4pm
Introduction
Legendhas it that in 1971, two college students at YaleUniversity used a large slingshot (madewith eight 2-metre
lengths of surgical rubber) to launch a loaf of frozen bread over their college master’s house. The approximate
trajectory of the loaf is shown below.
x
y
1.8m
75m 9m
9mMaster’sHouse
Figure 1: Approximate trajectory (not to scale)
The equations of motion that the bread satised are:
x(t0 + ∆t) = x0 + vx0∆t +
1
2ax (∆t)
2
y(t0 + ∆t) = y0 + vy0∆t +
1
2ay (∆t)
2
vx(t0 + ∆t) = vx0 + ax∆t
vy(t0 + ∆t) = vy0 + ay∆t
where x is the distance travelled in the horizontal direction, y is the distance travelled in the vertical direction,
vx is the velocity in the horizontal direction, vy is the velocity in the vertical direction, ax is the acceleration
in the horizontal direction, ay is the acceleration in the vertical direction, the subscript _0, denotes a value at
time t0 and ∆t is the time interval at which successive new values of x, y, vx and vy are computed. ax = 0 m s−2
and ay = −9.81 m s−2 (i.e. ay is the acceleration due to gravity).
Task 1
You need to write a program that computes the trajectory of the bread. When this program is invoked a user
must be able to select one of the following three options:
i for specifying initial conditions,
c for computing and plotting the trajectory, or
q for quitting the program.
A sample printout of the functioning program is given below.
1
i
1.8
30
.6
9
84
.1
c
q
>>> main()
Please specify one of the following options:
'q' - quit
'i' - input initial conditions
'c' - compute and plot trajectory
Input launch height (in meters):
Input launch velocity (in meters/second):
Input the launch angle (in radians):
Input height of master's house (in meters):
Input distance to house's furthest wall (in meters):
Input time increment for modelling (in seconds):
Please specify one of the following options:
'q' - quit
'i' - input initial conditions
'c' - compute and plot trajectory
Please specify one of the following options:
'q' - quit
'i' - input initial conditions
'c' - compute trajectory
You can initialise a vector in Python with the following type of command:
>>> x_vec = ( )
>>> x_vec
( )
You can add a new value to the vector with the following type of command:
>>> x_vec += (5,)
>>> x_vec
(5,)
You must round all values returned by the kinetic model to two decimal places.
It is not a requirement of the assignment to plot out your trajectory, but you are advised to do so in order to
check the plausibility of your results. You can use the following commands to plot the trajectory:
>>> import matplotlib.pyplot as plt
>>> plt.plot(x_vec, y_vec)
>>> plt.xlabel('Horizontal displacement (m)')
>>> plt.ylabel('Vertical displacement (m)')
>>> plt.show( )
If you plot the trajectory corresponding to the initial conditions above youwould obtain a graphwith the shape
shown below (though the scaling of the axes may be dierent). Before submitting your assignment make sure
you remove any plot commands as they can disrupt the automatic testing procedure. You must implement
your solution using the provided form for the equations. That is, you must compute the trajectory one sample
at a time.
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Note that you can assume the user will always enter the i option before entering the c option.
Task 2
Modify your program so that it takes in a fourth command option: o, which causes the program to determine
and print out the optimum launch angle. A sample printout when the o option is entered is given below:
o
>>> main()
Please specify one of the following options:
'q' - quit
'i' - input initial conditions
'c' - compute trajectory
'o' - print out optimum launch angle
0.85
Again, you can assume the user will have entered the i option before entering the o option. Note that in the
sample output above, 0.85 is not the correct value for the optimal angle; you need to write code which will
produce the correct optimal angle. You cannot simply print out an answer - there must be code written to
determine the optimal angle. You must also round the value for optimal angle to two decimal places.
Writing Your code
You must download the le, a1.py, from Blackboard, and write your code in that le. When you submit you
assignment youmust submit only one le and it must be called a1.py. Do not submit any other les or it can
disrupt the automatic code testing program which will grade your assignments.
Design
Your are expected to use good programming practice in your code and you must incorporate at least the fol-
lowing functions.
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Î main
This function handles the interaction of your program with the user and manages the calls to the other func-
tions you write. It also handles the plotting. It is invoked with the following command
>>> main()
Parameters
• None Takes no parameters
Returns
• None Does not return anything
Î get_initial_conditions
This function prompts the user to input the launch height, the launch velocity, the launch angle, the master’s
house height, the distance to the furthest wall of the master’s house and the time increment for modelling the
equations of motion. It is assumed that the initial horizontal position is 0.
Parameters
• None Takes no parameters
Returns
• x0 The initial horizontal position
• y0 The initial vertical position
• v0 The launch velocity
• theta0 The launch angle
• ax The acceleration in the x direction
• ay The acceleration in the y direction
• house_height The height of the master’s house
• house_distance The distance to the furthest wall of the house
• delta_t The time increment used to implement the modelling
Î kinetic_model
This function takes in the relevant initial conditions as arguments and uses the equations ofmotion to calculate
and return vectors of time-series results.
Parameters
• x0 The initial horizontal position
• y0 The initial vertical position
• v0 The launch velocity
• theta0 The launch angle
• ax The acceleration in the x direction
• ay The acceleration in the y direction
• house_height The height of the master’s house
• house_distance The distance to the furthest wall of the house
• delta_t The time increment used to implement the modelling
Returns
• x_vec Vector of x-coordinates
• y_vec Vector of y-coordinates
• vx_vec Vector of horizontal velocities
• vy_vec Vector of vertical velocities Note that the vector of y co-ordinatesmust not include any negative
values. i.e. do not include points with co-ordinates that are "below the ground".
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Assessment and Marking Criteria
Functionality Assessment 7 Marks
The functionality will be marked out of 7. Your assignment will be put through a series of tests and your
functionality mark will be proportional to the number of tests you pass. If, say, there are 25 functionality tests
and you pass 20 of them, then your functionality mark will be 20/25× 7.
You will be given the functionality tests before the due date for the assignment so that you can gain a good idea
of the correctness of your assignment yourself before submitting. You should, however, make sure that your
program meets all the specications given in the assignment. That will ensure that your code passes all the
tests. Note: Functionality tests are automated and so string outputs need to exactly match what is expected.
Code Style Assessment 3 Marks
The style of your assignment will be assessed by one of the tutors, and you will be marked according to the
style rubric provided with the assignment. The style mark will be out of 3.
Assignment Submission
You must submit your completed assignment electronically through Blackboard. The only le you submit
should be a single Python le called a1.py (use this name – all lower case). This should be uploaded to Black-
board > Assessment > Assignment 1. You may submit your assignment multiple times before the deadline –
only the last submission will be marked.
Late submission of the assignmentwill not be accepted. In the event of exceptional personal ormedical circum-
stances that prevent you from handing in the assignment on time, you may submit a request for an extension.
See the course prole for details of how to apply for an extension.
* Requests for extensionsmust bemade no later than 48 hours prior to the submission deadline. The application
and supporting documentation (e.g. medical certicate) must be submitted to the ITEE Coursework Studies
oce (78-425) or by email to [email protected]. If submitted electronically, youmust retain the original
documentation for a minimum period of six months to provide as verication should you be requested to do
so.
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