An aircraft flies at supersonic speed at Mach number $M = 2.1$ in standard air. What is the half-angle of the Mach cone (Mach angle $\mu$) in degrees?

Answer Key:

28.24,28.64

### 5-Stage Derivation & Analytical Solution: 1. **Stage 1: Governing Concept & Domain Context:** * This question evaluates **Grammar & Vocabulary** under *Verbal Aptitude* in GATE AE. 2. **Stage 2: Mathematical Derivation:** * By definition of Mach wave geometry in supersonic flow: $\sin\mu = \frac{a t}{V t} = \frac{1}{M} = \frac{1}{2.1} \implies \mu = \arcsin(0.4762) = 28.44^\circ$. 3. **Stage 3: Distractor Elimination Forensics:** * The evaluated correct answer is derived using standard physical equations. * Distractor values correspond to typical unit conversion omissions or inverted formulas. 4. **Stage 4: Common Student Trap:** * *Trap:* Calculating $\cos\mu = 1/M$ instead of $\sin\mu = 1/M$. *Reference: Philip G. Hill, Carl R. Peterson, Mechanics and Thermodynamics of Propulsion (Pearson).*

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