PHYS 165 Module 4 Exam Two-Dimensional
Kinematics Projectile Motion Official Practice
Exam Actual Exam 2026/2027 with Detailed
Rationales | Complete Exam-Style Questions | Pass
Guaranteed – A+ Graded
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SECTION 1: VECTORS IN 2D & COMPONENTS Q1 – Q10
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Question 1 of 50
A hiker walks 5.0 km in a straight line at 37° north of east across a flat plateau. How far east
does the hiker travel from the starting point?
A. 4.0 km ✓ CORRECT
B. 3.0 km
C. 5.0 km
D. 2.5 km
Correct Answer: A
Rationale: The eastward component of a displacement vector is found by multiplying the
magnitude by the cosine of the angle measured from the positive x-axis, so 5.0 km × cos(37°)
≈ 4.0 km. Many students incorrectly select 3.0 km because they confuse sine and cosine,
using sin(37°) instead of cos(37°) for the horizontal component. A reliable rule is that cosine
always gives the adjacent side relative to the reference angle.
Question 2 of 50
A force vector points into the second quadrant with an x-component of –6.0 N and a
y-component of +8.0 N. What is the magnitude of this force vector?
A. 6.0 N
B. 10.0 N ✓ CORRECT
C. 8.0 N
D. 14.0 N
Correct Answer: B
,Rationale: The magnitude of a vector is computed using the Pythagorean theorem, so the
magnitude equals √[(–6.0)² + (8.0)²] = √(36 + 64) = 10.0 N. A common trap is adding the
absolute values of the components to get 14.0 N, which ignores the orthogonal relationship
between the x and y directions. Always square each component, sum them, and take the
square root.
Question 3 of 50
Two displacement vectors are given in unit-vector notation: A = 3.0 î + 4.0 ĵ meters and B =
2.0 î – 5.0 ĵ meters. What is the resultant vector R = A + B ?
A. 5.0 î + 1.0 ĵ m
B. 1.0 î + 9.0 ĵ m
C. 5.0 î – 1.0 ĵ m ✓ CORRECT
D. 6.0 î – 20.0 ĵ m
Correct Answer: C
Rationale: Vector addition requires adding the respective components independently, so the
x-component becomes 3.0 + 2.0 = 5.0 m and the y-component becomes 4.0 + (–5.0) = –1.0
m. The incorrect choice 6.0 î – 20.0 ĵ m arises from multiplying the components instead of
adding them, which is a frequent algebraic error. When adding vectors, treat the î and ĵ
components as completely separate scalar sums.
Question 4 of 50
A small aircraft flies 200 km due east, then turns and flies 150 km due north to reach its
destination. What is the magnitude of the aircraft's total displacement from its starting point?
A. 200 km
B. 350 km
C. 150 km
D. 250 km ✓ CORRECT
Correct Answer: D
Rationale: Displacement is the straight-line distance from start to finish, so the magnitude
equals √(200² + 150²) = √(40000 + 22500) = 250 km. The answer 350 km represents the total
path length traveled, which confuses distance with displacement. Remember that
displacement depends only on the initial and final positions, not on the route taken.
Question 5 of 50
A surveyor measures a property line as a vector of magnitude 12.0 m oriented 60.0° above
the positive x-axis. What is the x-component of this vector?
A. 6.0 m ✓ CORRECT
, B. 10.4 m
C. 12.0 m
D. 8.5 m
Correct Answer: A
Rationale: The x-component is calculated as 12.0 m × cos(60.0°) = 12.0 m × 0.500 = 6.0 m.
The value 10.4 m represents the y-component, which students obtain when they mistakenly
apply sine to the angle for the horizontal direction. For angles measured from the positive
x-axis, cosine always yields the horizontal component and sine yields the vertical component.
Question 6 of 50
A velocity vector has a magnitude of 15 m/s and points into the second quadrant, where its
x-component is –9.0 m/s and its y-component is positive. What is the value of the
y-component?
A. 9.0 m/s
B. 12 m/s ✓ CORRECT
C. 15 m/s
D. 6.0 m/s
Correct Answer: B
Rationale: Using the Pythagorean relationship v² = v_x² + v_y², the y-component equals √(15²
– 9²) = √(225 – 81) = √144 = 12 m/s. Some students incorrectly select 9.0 m/s by assuming
the components are equal when the vector is in the second quadrant, which is not generally
true. The component formula v_y = √(v² – v_x²) works in any quadrant as long as you use the
squared values.
Question 7 of 50
A sailboat moves with velocity v = 4.0 î – 3.0 ĵ m/s. Measured counterclockwise from the
positive x-axis, what is the direction of this velocity vector?
A. 36.9°
B. 53.1°
C. 323.1° ✓ CORRECT
D. 216.9°
Correct Answer: C
Rationale: The angle is found from arctan(–3..0) = –36.9°, and since the vector lies in the
fourth quadrant (positive x, negative y), the standard counterclockwise angle is 360° – 36.9° =
323.1°. The answer 216.9° places the vector in the third quadrant, which is a common
sign-error trap when both components are negative. Always verify the quadrant by checking
the signs of the individual components before finalizing the angle.
Kinematics Projectile Motion Official Practice
Exam Actual Exam 2026/2027 with Detailed
Rationales | Complete Exam-Style Questions | Pass
Guaranteed – A+ Graded
══════════════════════════════════════
SECTION 1: VECTORS IN 2D & COMPONENTS Q1 – Q10
══════════════════════════════════════
Question 1 of 50
A hiker walks 5.0 km in a straight line at 37° north of east across a flat plateau. How far east
does the hiker travel from the starting point?
A. 4.0 km ✓ CORRECT
B. 3.0 km
C. 5.0 km
D. 2.5 km
Correct Answer: A
Rationale: The eastward component of a displacement vector is found by multiplying the
magnitude by the cosine of the angle measured from the positive x-axis, so 5.0 km × cos(37°)
≈ 4.0 km. Many students incorrectly select 3.0 km because they confuse sine and cosine,
using sin(37°) instead of cos(37°) for the horizontal component. A reliable rule is that cosine
always gives the adjacent side relative to the reference angle.
Question 2 of 50
A force vector points into the second quadrant with an x-component of –6.0 N and a
y-component of +8.0 N. What is the magnitude of this force vector?
A. 6.0 N
B. 10.0 N ✓ CORRECT
C. 8.0 N
D. 14.0 N
Correct Answer: B
,Rationale: The magnitude of a vector is computed using the Pythagorean theorem, so the
magnitude equals √[(–6.0)² + (8.0)²] = √(36 + 64) = 10.0 N. A common trap is adding the
absolute values of the components to get 14.0 N, which ignores the orthogonal relationship
between the x and y directions. Always square each component, sum them, and take the
square root.
Question 3 of 50
Two displacement vectors are given in unit-vector notation: A = 3.0 î + 4.0 ĵ meters and B =
2.0 î – 5.0 ĵ meters. What is the resultant vector R = A + B ?
A. 5.0 î + 1.0 ĵ m
B. 1.0 î + 9.0 ĵ m
C. 5.0 î – 1.0 ĵ m ✓ CORRECT
D. 6.0 î – 20.0 ĵ m
Correct Answer: C
Rationale: Vector addition requires adding the respective components independently, so the
x-component becomes 3.0 + 2.0 = 5.0 m and the y-component becomes 4.0 + (–5.0) = –1.0
m. The incorrect choice 6.0 î – 20.0 ĵ m arises from multiplying the components instead of
adding them, which is a frequent algebraic error. When adding vectors, treat the î and ĵ
components as completely separate scalar sums.
Question 4 of 50
A small aircraft flies 200 km due east, then turns and flies 150 km due north to reach its
destination. What is the magnitude of the aircraft's total displacement from its starting point?
A. 200 km
B. 350 km
C. 150 km
D. 250 km ✓ CORRECT
Correct Answer: D
Rationale: Displacement is the straight-line distance from start to finish, so the magnitude
equals √(200² + 150²) = √(40000 + 22500) = 250 km. The answer 350 km represents the total
path length traveled, which confuses distance with displacement. Remember that
displacement depends only on the initial and final positions, not on the route taken.
Question 5 of 50
A surveyor measures a property line as a vector of magnitude 12.0 m oriented 60.0° above
the positive x-axis. What is the x-component of this vector?
A. 6.0 m ✓ CORRECT
, B. 10.4 m
C. 12.0 m
D. 8.5 m
Correct Answer: A
Rationale: The x-component is calculated as 12.0 m × cos(60.0°) = 12.0 m × 0.500 = 6.0 m.
The value 10.4 m represents the y-component, which students obtain when they mistakenly
apply sine to the angle for the horizontal direction. For angles measured from the positive
x-axis, cosine always yields the horizontal component and sine yields the vertical component.
Question 6 of 50
A velocity vector has a magnitude of 15 m/s and points into the second quadrant, where its
x-component is –9.0 m/s and its y-component is positive. What is the value of the
y-component?
A. 9.0 m/s
B. 12 m/s ✓ CORRECT
C. 15 m/s
D. 6.0 m/s
Correct Answer: B
Rationale: Using the Pythagorean relationship v² = v_x² + v_y², the y-component equals √(15²
– 9²) = √(225 – 81) = √144 = 12 m/s. Some students incorrectly select 9.0 m/s by assuming
the components are equal when the vector is in the second quadrant, which is not generally
true. The component formula v_y = √(v² – v_x²) works in any quadrant as long as you use the
squared values.
Question 7 of 50
A sailboat moves with velocity v = 4.0 î – 3.0 ĵ m/s. Measured counterclockwise from the
positive x-axis, what is the direction of this velocity vector?
A. 36.9°
B. 53.1°
C. 323.1° ✓ CORRECT
D. 216.9°
Correct Answer: C
Rationale: The angle is found from arctan(–3..0) = –36.9°, and since the vector lies in the
fourth quadrant (positive x, negative y), the standard counterclockwise angle is 360° – 36.9° =
323.1°. The answer 216.9° places the vector in the third quadrant, which is a common
sign-error trap when both components are negative. Always verify the quadrant by checking
the signs of the individual components before finalizing the angle.
