MAE 30A Homework 9
Written homework must be submitted as a single pdf document via Gradescope. Late
submissions up to 24 hours of the due time will be accepted for up to 80% credit per the course
syllabus. Submissions beyond 24 hours of the due time will receive 1% credit. Please ensure all
diagrams and calculations are neatly written in order to receive full points.
A Note About the Guidance Prompts
Some homework problems (usually the more challenging ones) will be accompanied by a set of
guidance questions. These prompts provide guidance and insight into the thought process
behind solving problems. You do not need to submit any written answers for the guidance
prompts along with the homework, and we hope you use them to exercise thinking aloud
techniques for better conceptual mastery of the knowledge, and prepare for assessments such
as quizzes and exams. We suggest that you follow the prompts in the advised order, particularly
in terms of before, during, or after the computational process - this will provide additional insight
and aid in your understanding of the thought process behind the calculation process.
Bonus: Group Discussion video submission on Canvas
Why group discussion?
Peer discussion is a powerful learning tool that enhances understanding of a subject.There are
two key elements in a group discussion - explain and receive feedback. To explain a concept
clearly to peers, you will think aloud and think in-depth. The feedback probes your thought
process and may encourage you to rethink your reasoning or problem-solving approach.
Listening to others and providing feedback also requires in-depth thinking. This interaction
creates a great opportunity for higher-order thinking and mastering knowledge for all
participants in a group discussion. This process also helps to improve technical communication
skills.
Earn bonus for group study in MAE 30A
To earn extra credits for group study in MAE 30A, here are the steps and criteria
1. Sign up for a study group on Canvas -> People -> Study Group for the appropriate
assignment; please do so for each assignment. Each group can have up to 3 people.
2. Hold a meaningful group discussion on the assignment questions and any other topic
you think is worth discussing for the relevant course content (challenging topics in that
week, quiz/exam prep, etc). You can meet either in person or remotely; in either case,
you can use Zoom to record the video. The video does not need to be perfectly polished,
and there is no need to re-record anything.
3. Submit the video to Canvas through the designated submission link.One video per
group. Submissions are due at the same time as the written homework assignment.
4. Your video will be only viewed by the course instructional team members.
5. Each group member must lead discussion for at least one different question. The
discussion will start from one question led by the question leader, the rest of the group
actively provide feedback and raises questions. Once done with one question, another
student will lead the discussion for the next question, until everyone in the group has the
chance to lead at least one discussion.
6. You are welcome to use the guidance prompts as the basis of your discussion; but you
are also more than welcome to extend your discussion of the topic if you feel the
prompts are too limiting. Whenever the group gets stuck in discussion, we encourage
you to go back to lecture and discussion materials for reference. If after a thorough
discussion, the group still can not figure out the answer or is not sure, it is time to go to
office hours!
A sample group discussion video, based on prompts similar to those on the homework, can be
found on Canvas -> Pages -> Group Discussion Video. We encourage one student to screen
share the problem and use the annotation tools as needed (This can be seen in the example
video). Do not feel the need to be constrained by our example. We are looking for a meaningful
and relevant discussion where students are helping each other learn.
Problem 1 (100 points)
Problem Description
In a boat race, boat A is leading boat B by 50 m and both boats are traveling at a constant
speed of 180 km/h. At t = 0, the boats accelerate at constant rates. Knowing that when B
passes A, t = 8 s and Va = 225 km/h, determine (a) the acceleration of A, (b) the acceleration of
B.
Problem 2 (100 points)
Problem Description
The elevator shown in the figure moves downward with a constant velocity of 4 m/s. Determine
(a) the velocity of the cable C, (b) the velocity of the counterweight W, (c) the relative velocity of
the cable C with respect to the elevator, (d) the relative velocity of the counterweight W with
respect to the elevator.
Problem 3 (100 points)
Problem Description
A baseball pitching machine “throws” baseballs with a horizontal velocity v0. Knowing that height
h varies between 788 mm and 1068 mm, determine (a) the range of values of v0, (b) the values
of α corresponding to h = 788 mm and h = 1068 mm.
Problem 4 (100 points)
Problem Description (this is the part you need to submit)
Guidance Prompts (these are resources for you to solve problems and think aloud)
These prompts are supposed to provide guidance and insight into the thought process behind
problem-solving. You do not need to submit any written answers for the guidance prompts
along with the homework, and we hope you use them to exercise thinking aloud techniques
for better conceptual mastery of the knowledge, and prepare for assessments such as quizzes
and exams. Please note that guidance prompts 1 are to be thought of before solving the
problem, while guidance problems 2 are to be thought of after solving the problem.
1. Before solving the main problem, try to think about the following questions:
a. Which bodies/objects are in motion relative to each other?
b. How can you mathematically relate the velocity of the wind with the velocity of the
boat? Which velocities are absolute, and which are relative?
c. Which velocity has a direction related to the angle of the flag shown in the figure?
d. Does the absolute velocity of the wind change as the boat travels in a different
direction? What about the relative velocity of the wind with respect to the boat?
Problem 5 (100 points)
Problem Description (this is the part you need to submit)
Guidance Prompts (these are resources for you to solve problems and think aloud)
These prompts are supposed to provide guidance and insight into the thought process behind
problem-solving. You do not need to submit any written answers for the guidance prompts
along with the homework, and we hope you use them to exercise thinking aloud techniques
for better conceptual mastery of the knowledge, and prepare for assessments such as quizzes
and exams. Please note that guidance prompts 1 are to be thought of before solving the
problem, while guidance problems 2 are to be thought of after solving the problem.
1. Before solving the main problem, try to think about the following questions:
a. Tangent to the direction of travel, knowing that the speed increases at a constant
rate, what type of motion is occuring? How would you determine the acceleration
along the tangent direction?
b. How would you determine the tangential speed of the car after a given time t?
What allows you to apply such an equation?
c. When an object undergoes curvilinear motion (i.e. it turns), there must be
nonzero acceleration in which direction of the motion? How can you obtain the
total acceleration for an object that is undergoing curvilinear motion?
d. Which component of total acceleration does tangential speed affect? How does
tangential acceleration contribute to total acceleration?
Problem 6 (100 points)
Problem Description (this is the part you need to submit)
Guidance Prompts (these are resources for you to solve problems and think aloud)
These prompts are supposed to provide guidance and insight into the thought process behind
problem-solving. You do not need to submit any written answers for the guidance prompts
along with the homework, and we hope you use them to exercise thinking aloud techniques
for better conceptual mastery of the knowledge, and prepare for assessments such as quizzes
and exams. Please note that guidance prompts 1 are to be thought of before solving the
problem, while guidance problems 2 are to be thought of after solving the problem.
1. Before solving the main problem, try to think about the following questions:
a. Where is relative motion present? How can we relate this relative motion to the
absolute motion of each object?
b. How can you define the relative velocity and relative acceleration of the
parasailer with respect to the boat? Is it easier to define this in a rectilinear
coordinate system or in a radial-transverse curvilinear coordinate system? How
are those two coordinate systems related to each other?
c. Compare the standard Cartesian coordinate system to the radial-transverse
coordinate system. Do the coordinate directions remain constant over time for
both coordinate systems?