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Vector Resolution Worksheet

Worksheet
Grade 12
English (UK)

Vector Resolution Worksheet

Multiple Choice Questions

  1. What is the horizontal component of a 50 N force acting at 30° above the horizontal?
a) 25 N
b) 43.3 N
c) 50 N
d) 35.4 N
  1. A force of 100 N acts at an angle of 60° to the horizontal. What is the vertical component?
a) 50 N
b) 86.6 N
c) 70.7 N
d) 100 N
  1. Which trigonometric function is used to find the component of a vector parallel to the angle given?
a) Sine
b) Cosine
c) Tangent
d) Cotangent
  1. A vector of 80 N is acting at 45° to the horizontal. What is the magnitude of its horizontal component?
a) 56.6 N
b) 80 N
c) 40 N
d) 65.3 N
  1. If a vector is resolved into two perpendicular components, what is the relationship between the magnitude of the vector and its components?
a) The vector is the sum of the components
b) The vector is the product of the components
c) The vector is equal to the difference of the components
d) The vector is the square root of the sum of the squares of the components
  1. What is the vertical component of a 60 N vector acting at 0° to the horizontal?
a) 60 N
b) 0 N
c) 30 N
d) 42.4 N
  1. When resolving a vector, what do the horizontal and vertical components represent?
a) The total force in each direction
b) The angle of the vector
c) The magnitude of the original vector
d) The resultant vector
  1. A force of 90 N acts at 30° to the horizontal. What is the value of its vertical component?
a) 45 N
b) 77.9 N
c) 60 N
d) 90 N
  1. Which of the following best describes vector resolution?
a) Adding two vectors
b) Splitting a vector into perpendicular components
c) Multiplying two vectors
d) Finding the magnitude of a vector
  1. If a force of 70 N acts at 60° to the horizontal, what is the horizontal component?
a) 35 N
b) 60.6 N
c) 70 N
d) 40.5 N

Open-Ended Questions

  1. Explain the process of resolving a vector into its horizontal and vertical components, including the trigonometric functions involved.
  1. A force of 120 N acts at an angle of 25° above the horizontal. Calculate the horizontal and vertical components.
  1. Describe a real-world engineering scenario where vector resolution is essential, and explain why.
  1. Given a vector of 150 N at 40° to the horizontal, show step-by-step calculations for both components.
  1. Why is it important to resolve forces when analysing structures in engineering?
  1. A force of 200 N acts downward at 70° to the horizontal. Calculate its vertical and horizontal components.
  1. How can incorrect vector resolution affect the outcome of an engineering project? Provide an example.
  1. A force of 50 N is acting at 120° from the positive x-axis. Calculate its horizontal and vertical components.
  1. Discuss the difference between vector addition and vector resolution, with examples.
  1. Given a resultant force and one component, explain how to determine the other component using vector resolution principles.