GATE 2025 AE – Question 54
While taking off, the net external force acting on an airplane during the ground roll segment can be assumed to be constant. The airplane starts from rest. $S_{LO}$ and $V_{LO}$ are the ground roll distance and the lift-off speed, respectively. $\alpha V_{LO}$ ($\alpha > 0$) denotes the airplane speed at $0.5\,S_{LO}$. Neglecting changes in the airplane mass during the ground roll segment, the value of $\alpha$ is _____ (rounded off to two decimal places).
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Correct answer: 0.70 to 0.72
Explanation
With constant force and mass the acceleration is constant, so $V^2 = 2as$. Half the distance gives $V^2 = \frac{1}{2}V_{LO}^2$, so $\alpha = \frac{1}{\sqrt 2} = 0.71$.