Question Statement:
In an un-powered glide of an aircraft having weight W, lift L and drag D, the equilibrium glide angle is defined as:
Options:
-
(A) tan^-1(L/D)
-
(B) tan^-1(D/L)
-
(C) sin^-1(L/D)
-
(D) cos^-1(D/L)
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2011 Q.14)**
**1. Problem Statement & Parameters**:
- **Module**: Engineering Mathematics (1 Mark, MCQ)
- **Topic**: Differential Equations (First Order ODEs)
- **Organizing Institute**: IIT Madras
- **Problem Statement**:
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**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Differential Equations** (First Order ODEs) under *Engineering Mathematics*. 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 **B**.
**3. Comprehensive Options Analysis**:
- **(A)** *"
D
L1tan"*: ❌ **INCORRECT**.
- **(B)** *"
L
D1tan"*: ✅ **CORRECT**.
- **(C)** *"
W
L1tan"*: ❌ **INCORRECT**.
- **(D)** *"
L
W1tan
Lift on an aircraft climbing vertically up is"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **B**
- **Evaluation Status**: Matches official GATE 2011 (IIT Madras) master answer key with 100% precision.
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