EXAM1_PHYS206(HONORS)
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School
Texas A&M University *
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Course
206
Subject
Mathematics
Date
Apr 3, 2024
Type
Pages
2
Uploaded by EarlRoseTarsier36
Problem Prompt (with figure if necessary): Two friends, Jay and Akhil, walk back home after playing basketball together. Jay walks 23 m, at an angle of 23
°
North of West, while Akhil walks 18m, at an angle of 47
°
East of North. Find the distance between them. A)
24.38m B)
34.49m, LOs –
1, 2, 9 C)
8.66m, LOs –
1, 2 D)
9.83m E)
22.72m, LOs –
1,9 Solution: Note: This picture is only for reference, not to be included in question. Turn each of the vectors into its component forms. Jay →
−23 cos(23°)𝚤 , 23sin (23°)𝑗.
Akhil →
18 sin(47°) 𝚤, 18 cos(47°) 𝑗.
Now, SUBTRACT the vector components to find the new coordinates
. 18 sin(47°) − (−23 cos(23°)), 18 cos(47°) − 23sin (23°)
13.16 − (−21.17), 12.28 − 8.99
34.33𝚤, 3.29𝑗
Take the components and convert into a vector to find distance. √(??. ??)
?
+ (?. ?𝟗)
?
√1189.37
??. ?𝟗𝒎
LO’s assigned to each answer: A –
Random Answer B –
Correct Answer
, LO1:
Correctly breaks up the components of each vector.
LO2: Computes the relevant operations on the vector components(subtraction). LO9: Recognizes that one of the vectors lies in Quadrant II, therefore having a negative X(-x) component.
C –
Partial Credit (fails to recognize the negative x component)
, LO1:
Correctly breaks up the components of each vector.
LO2: Computes the relevant operations on the vector components(subtraction). D –
Random Answer
E –
Partial Credit (Addition instead of subtraction),
LO1:
Correctly breaks up the components of each vector. LO9: Recognizes that one of the vectors lies in Quadrant II, therefore having a negative X(-x) component. Answer the following questions for this submitted problem (1 point each): 1.
Why is this appropriate content for Exam1? a.
It involves the basics and fundamentals of Exam1, which relies heavily on vectors. With a solid understanding of vectors and the coordinate system 2.
Why is this topic important for 206 students to understand? How will this content be applied to future careers of 206 students? a.
Understanding vectors and the coordinate system is very important to PHYS 206. With a solid understanding of both concepts, students are able to manipulate and use each concept that can be applied to later units. Ex: For a force problem, manipulating the coordinate system and breaking the gravity vector makes the problem easier and makes calculations easier. 3.
What are common misconceptions and preconceptions about this topic? a.
Everything lies in the positive plane of the coordinate system. If students take a minute to understand the problem and visualize it, many mistakes can be avoided. 4.
Classify the problem based on the description in the Honors Assignment Description file (Level 1, 2 or 3) a.
Between Level 1 and 2. Although, it involves simple addition and distance formula, understanding the coordinate system and the angles associated with each vector can be confusing. That being said, I expect majority of the students to get this problem correct. 5.
What percentage of students do you think would get this problem fully correct on the exam? What percentage of students do you think would get either full or partial credit for this problem on the exam? a.
I expect around 60% of students achieving full credit, while 85% select an answer choice that receives partial credit.
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