Unit notes and practice questions
Everything here is for unit 2 of the Grade 11 Physics textbook: what the chapter covers, the short notes, practice questions with their answers, and the lesson video where one exists.
The cards filed under this chapter on the Grade 11 Physics page. Open one at a time.
When you use it
Use this when you find the direction of a resultant from tan inverse of R_y over R_x and report it as an angle from the x axis.
Watch out
A calculator tan^-1 gives an angle only between -90 and 90 degrees. Check the signs of R_x and R_y on the xy plane and place the angle in the correct quadrant. For example, a negative R_x with a positive R_y lies above the negative x axis, not the positive x axis.
Drafted from Grade 11 Physics, pages 17-46, then checked twice before it went up
When you use it
Use this to resolve a vector into its x and y components when the angle is measured from the positive x axis.
Watch out
If the angle is measured from the y axis instead, the cosine goes with the y component and the sine with the x component.
Drafted from Grade 11 Physics, pages 17-46, then checked twice before it went up
When you use it
Use this after adding vectors by the component method, when you need the size of the resultant vector.
Drafted from Grade 11 Physics, pages 17-46, then checked twice before it went up
When you use it
Use this when you add two vectors that do not point in the same direction and need the magnitude of the resultant.
Watch out
The magnitude of A+B equals |A|+|B| only when the vectors are parallel. A 3 N force and a 4 N force at right angles give a resultant of 5 N, not 7 N.
Drafted from Grade 11 Physics, pages 17-46, then checked twice before it went up
When you use it
Use this to find the angle between two vectors or to calculate work and power from a force and a displacement or velocity.
Watch out
The dot product is a scalar, not a vector, so its answer has no direction. Place the vectors tail to tail before reading the angle.
Drafted from Grade 11 Physics, pages 17-46, then checked twice before it went up
10 multiple-choice questions written against this chapter, each with its answer and the reason. Try one before you open the answer.
Question 1
Which of the following physical quantities is a vector quantity?
Answer: A Velocity
Why
A vector quantity has both magnitude and direction. Velocity has both magnitude and direction, while speed, volume, and power are scalar quantities described by magnitude alone.
Question 2
If a displacement vector is 60 km toward North, what is its negative vector?
Answer: A 60 km toward South
Why
The negative of a vector has the exact same magnitude as the original vector but points in the opposite direction. Opposite to North is South.
Question 3
A boat sails downstream in the Baro River. The boat moves at 0.50 m/s in still water, and the river flows in the same direction at 0.30 m/s. What is the resultant velocity of the boat?
Answer: A 0.80 m/s, downstream
Why
When two collinear vectors point in the same direction, their magnitudes add directly: R = 0.50 m/s + 0.30 m/s = 0.80 m/s, downstream.
Question 4
What is the scalar (dot) product of any unit vector with itself, such as i · i?
Answer: A 1
Why
The dot product of a unit vector with itself is unity (1) because both vectors have a magnitude of 1 and the angle between them is 0 degrees (cos 0° = 1).
Question 5
According to the triangle law of vector addition, how must two vectors be connected to find their resultant?
Answer: A Head to tail
Why
In the triangle law of vector addition, vectors are placed head to tail, and the resultant vector is drawn from the tail of the first vector to the head of the second.
Question 6
An ant walks 40 cm due South and then 50 cm due West. What is the magnitude of the ant's resultant displacement from its starting point?
Answer: A 64 cm
Why
Because the two displacements are perpendicular, use the Pythagorean theorem: S = √(402 + 502) = √(1600 + 2500) = √4100 ≈ 64 cm.
Question 7
A pushing force of magnitude 35 N acts at an angle of 40° above the negative x-axis. If cos 40° = 0.766, what is the magnitude of the x-component of this force?
Answer: A 26.8 N
Why
The x-component is given by Fx = F cos 40° = 35 N × 0.766 = 26.8 N.
Question 8
A force F = (5i + 3j) N moves a block along a displacement S = (-2i + 4j) m in Hawassa. What is the work done by the force?
Answer: A 2 J
Why
Work is the dot product of force and displacement: W = F · S = (5)(-2) + (3)(4) = -10 + 12 = 2 J.
Question 9
Given the force vector F = (12i - 16j) N, what is the unit vector in the direction of F?
Answer: A 0.6i - 0.8j
Why
The magnitude of F is √(122 + (-16)2) = √(144 + 256) = √400 = 20. The unit vector is (12/20)i - (16/20)j = 0.6i - 0.8j.
Question 10
An unknown vector D is added to C = (-4i + 5j) units so that the resultant R = C + D is (-i + j) units. What is vector D?
Answer: A (3i - 4j) units
Why
For components: Rx = Cx + Dx → -1 = -4 + Dx → Dx = 3, and Ry = Cy + Dy → 1 = 5 + Dy → Dy = -4. Therefore, D = (3i - 4j) units.
The app holds 12 questions on this unit, marked as you go. These are the first 10.
Unit 2 runs from page 17 to page 46 of the Ministry of Education edition.
Ministry of Education edition, English, 338 pages
Temari turns this chapter into timed practice and marks it as you go, with an AI tutor to explain anything that did not land.
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