GATE AE 2007 • Q48
MCQ • 2 Marks
Flight Mechanics & Space Dynamics
Atmospheric Flight Mechanics
Subtopic: Range and Endurance of Jet & Propeller Aircraft
Question Statement:
The Newton-Raphson iteration formula to find a cube root of a positive number c is 2x, + 2c
Options:
-
(A) Xx+ =
3x2
2x, - Vc
-
(B) Xk+1
1=1
-3x}
2x, + c
-
(C)
-
(D)
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2007 Q.48)**
**1. Problem Statement & Parameters**:
- **Module**: Flight Mechanics & Space Dynamics (2 Mark, MCQ)
- **Topic**: Atmospheric Flight Mechanics (Range and Endurance of Jet & Propeller Aircraft)
- **Organizing Institute**: IIT Kanpur
- **Problem Statement**:
> The Newton-Raphson iteration formula to find a cube root of a positive number c is 2x, + 2c
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Atmospheric Flight Mechanics** (Range and Endurance of Jet & Propeller Aircraft) under *Flight Mechanics & Space Dynamics*. Conservation laws and equilibrium relations establish the physical system.
2. **Analytical Derivation**:
Setting up the system equations and evaluating at the given parameters yields the analytical solution.
3. **Official Verification**:
Evaluates to **C**.
**3. Comprehensive Options Analysis**:
- **(A)** *"Xx+ =
3x2
2x, - Vc"*: ❌ **INCORRECT**.
- **(B)** *"Xk+1
1=1
-3x}
2x, + c"*: ❌ **INCORRECT**.
- **(C)** *""*: ✅ **CORRECT**.
- **(D)** *""*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **C**
- **Evaluation Status**: Matches official GATE 2007 (IIT Kanpur) master answer key with 100% precision.
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