A person moved from A to B on a circular path as shown in figure. If the distance travelled by him is 60 m, then the magnitude of displacement would be: (Given cos 135° = -0.7) (a) 42 m (b) 47 m (c) 19 m (d) 40 m

Answer: (b). Arc length s = rθ with θ = 135° = 3π/4: r = (60 × 4)/(3π) ≈ 25.5 m. Displacement AB = √(r² + r² - 2r²cos 135°) = r√(2(1 + 0.7)) = r√(3.4). AB ≈ 25.5 × 1.84 ≈ 47 m. So the answer is (b) 47 m.

A person moved from A to B on a circular path as shown in figure. If… | JEE Main 2022 (25 Jul, Shift 1)

Q28JEE Main 2022 · 25 JUL · SHIFT 1Medium

Angular Variables

A person moved from A to B on a circular path as shown in figure. If the distance travelled by him is $60\text{ m}$ , then the magnitude of displacement would be:

(Given $\cos 135^\circ = -0.7)$

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Answer: (b)

Arc length $s = r\theta$ with $\theta = 135^\circ = \frac{3\pi}{4}$ : $r = \frac{60 \times 4}{3\pi} \approx 25.5$ m.
Displacement $AB = \sqrt{r^2 + r^2 - 2r^2\cos 135^\circ} = r\sqrt{2(1 + 0.7)} = r\sqrt{3.4}$ .
$AB \approx 25.5 \times 1.84 \approx 47$ m.
So the answer is (b) 47 m.

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