Lesson Worksheet: Resultant of Two Forces Mathematics

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In this worksheet, we will practice finding the resultant of two forces acting on one point and finding the direction of the resultant.

Q1:

Two forces of magnitudes 35 N and 91 N are acting at a particle. Given that the resultant is perpendicular to the first force, find the magnitude of the resultant.

  • A14√61 N
  • B126 N
  • C90 N
  • D84 N

Q2:

Two forces 𝐹=39 N and 𝐹=39√2 N act at a point. The measure of the angle between them is 45∘. Determine 𝑅, the magnitude of their resultant, and find 𝜃, the measure of the angle between their resultant and 𝐹. Give your answer to the nearest minute.

  • A𝑅=39√5N, 𝜃=1826′∘
  • B𝑅=39√5N, 𝜃=2634′∘
  • C𝑅=78N, 𝜃=1826′∘
  • D𝑅=78N, 𝜃=2634′∘

Q3:

Two perpendicular forces, F and F, act at a point. Their resultant, R, has magnitude 188 N and makes an angle of 60∘ with F. Find the magnitudes of F and F.

  • AF=47N, F=47N
  • BF=47N, F=47√3N
  • CF=94N, F=47√3N
  • DF=94N, F=94√3N

Q4:

The measure of the angle between two forces is 120∘ and the magnitude of their resultant is 79 N. Find their magnitudes, given that they have a difference of 51 N.

  • A10 N, 61 N
  • B35 N, 86 N
  • C40 N, 91 N
  • D14 N, 65 N

Q5:

Two forces of magnitudes 15 kg-wt and 7 kg-wt act as shown in the diagram. Determine 𝑅, the magnitude of the resultant, and find 𝜃, the measure of the angle between the resultant and due east.

  • A𝑅=19.1kg-wt, 𝜃=379′∘
  • B𝑅=15.74kg-wt, 𝜃=2956′∘
  • C𝑅=13kg-wt, 𝜃=2748′∘
  • D𝑅=14.88kg-wt, 𝜃=4829′∘

Q6:

Two perpendicular forces of magnitudes 88 N and 44 N act at a point. Their resultant makes an angle 𝜃 with the 88 N force. Find the value of sin𝜃.

  • A√55
  • B2
  • C12
  • D2√55

Q7:

Two forces of magnitudes 6𝐹 and 12𝐹 act at a point. The magnitude of their resultant is 9𝐹. Find the measure of the angle between them, giving your answer to the nearest minute.

  • A1106′∘
  • B13326′∘
  • C4326′∘
  • D206′∘

Q8:

Forces of magnitudes 22 N and 42 N act at a point. What is the maximum possible value of their resultant?

Q9:

Two forces, both of magnitude 𝐹N, act at the same point. The magnitude of their resultant is 90 N. When the direction of one of the forces is reversed, the magnitude of their resultant is 90 N. Determine the value of 𝐹.

  • A𝐹=90√2
  • B𝐹=45√2
  • C𝐹=3√5
  • D𝐹=90

Q10:

The angle between forces F and F is 112∘, and the measure of the angle between their resultant and F is 56∘. If the magnitude of F is 28 N, what is the magnitude of F?

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