The three forces F₁, F₂ and F₃ are acting on a particle. F₁ = (25i + 12j) N F₂ = (−7i − 5j) N F₃ = (15i − 28j) N The unit vectors i and j are horizontal and vertical respectively. The resultant of these three forces is F newtons. (a) (i) Find the magnitude of F, giving your answer to three significant figures.

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The three forces F₁, F₂ and F₃ are acting on a particle - AQA - A-Level Maths Pure - Question 13 - 2017 - Paper 2

Question 13

The three forces F₁, F₂ and F₃ are acting on a particle. F₁ = (25i + 12j) N F₂ = (−7i − 5j) N F₃ = (15i − 28j) N The unit vectors i and j are horizontal and vertic... show full transcript

Worked Solution & Example Answer:The three forces F₁, F₂ and F₃ are acting on a particle - AQA - A-Level Maths Pure - Question 13 - 2017 - Paper 2

Step 1

Sum the forces

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Answer

To find the resultant force F, we sum the vectors F₁, F₂, and F₃:

$F = F₁ + F₂ + F₃$

Substituting the values, we get:

$F = (25i + 12j) + (-7i - 5j) + (15i - 28j)$

Now, calculate the components:

$F = (25 - 7 + 15)i + (12 - 5 - 28)j$

Thus,

$F = 33i - 21j$

Step 2

Find the magnitude of F

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Answer

Next, we use the Pythagorean theorem to find the magnitude of the vector F:

$|F| = \\sqrt{(33)^2 + (-21)^2}$

Calculating this gives:

$|F| = \\sqrt{1089 + 441} = \\sqrt{1530}$

Evaluating the square root, we have:

$|F| \approx 39.1$ N (to three significant figures: 39.1 N)

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