Topic: Engineering Mathematics
A point P moves along the path y = x² – 4. What is the displacement when the point moves from x = 1 to x = 3?
- A. 8.24, @tan⁻¹(4)°
- B. 2, @tan⁻¹(1)°
- C. 11.3, @tan⁻¹(4)°
- D. 11.3, @tan⁻¹(1)°
Answer: A. 8.24, @tan⁻¹(4)°
Explanation: At x₁=1, y₁ = 1²-4 = -3. At x₂=3, y₂ = 3²-4 = 5. Displacement = √((x₂-x₁)² + (y₂-y₁)² ) = √((3-1)² + (5-(-3))²) = √(2² + 8²) = √68 ≈ 8.24. The angle is tan⁻¹((y₂-y₁)/(x₂-x₁)) = tan⁻¹(8/2) = tan⁻¹(4).