BMST Vectors and Resultant Forces — Questions and Answers
Question 1: Two forces act on an object: 30 N to the east and 40 N to the north. What is the magnitude of the resultant force?
- 50 N (Correct answer)
- 70 N
- 35 N
- 10 N
Correct answer: 50 N
For perpendicular forces, use the Pythagorean theorem: R = √(30² + 40²) = √(900 + 1600) = √2500 = 50 N.
Question 2: A vector quantity differs from a scalar quantity in that a vector has:
- Both magnitude and direction (Correct answer)
- Only magnitude
- Only direction
- Neither magnitude nor direction
Correct answer: Both magnitude and direction
Vectors have both magnitude (size) and direction (e.g., 10 m/s north). Scalars have only magnitude (e.g., 10 m/s with no direction specified).
Question 3: A force of 100 N is applied at a 30° angle to the horizontal. What is the horizontal component of this force?
- 86.6 N (Correct answer)
- 50 N
- 100 N
- 57.7 N
Correct answer: 86.6 N
Horizontal component = F × cos(θ) = 100 × cos(30°) = 100 × (√3/2) ≈ 86.6 N.
Question 4: If two vectors point in exactly opposite directions and have equal magnitudes, what is the magnitude of their resultant?
- 0 (Correct answer)
- Equal to one of the magnitudes
- Double one magnitude
- Cannot be determined
Correct answer: 0
Vectors in exactly opposite directions cancel each other. If both have magnitude A, the resultant = A − A = 0. This represents a state of equilibrium.
Question 5: Which of the following is an example of a vector quantity?
- Velocity (Correct answer)
- Temperature
- Mass
- Speed
Correct answer: Velocity
Velocity is a vector because it includes both magnitude (how fast) and direction (which way). Temperature, mass, and speed are scalars — they have magnitude only.
Question 6: A vertical force of 60 N and a horizontal force of 80 N act on the same point. What is the angle the resultant makes with the horizontal?
- 36.9° (Correct answer)
- 53.1°
- 45°
- 30°
Correct answer: 36.9°
tan(θ) = opposite/adjacent = 60/80 = 0.75. θ = arctan(0.75) ≈ 36.9°. The resultant is 100 N (using Pythagorean theorem) at 36.9° above horizontal.
BMST Vectors and Resultant Forces
Two forces act on an object: 30 N to the east and 40 N to the north.
What is the magnitude of the resultant force?