Gimli Glider

Aircraft Boeing 767 lose both engines at 35000 feet. The plane captain maintains optimum gliding conditions. Every minute, lose 2100 feet and maintain constant speed 201 knots.

Calculate how long it takes for a plane to hit the ground from engine failure. Calculate how far the pilot glides the plane.

1 foot = 1 ft = 0.3 m
1 knot = 1.9 km/h

Correct answer:

t =  16.7 min
s =  105.5 km

Step-by-step explanation:

$$\begin{gathered} h=35000\text{ft} \\ {s}_1=h\to \text{km}=h:3281\text{km}=35000:3281\text{km}=10.668\text{km} \\ {v}_y=2100\text{ft/min} \\ h=v_y\cdot t \\ t=\frac{h}{v_y}=\frac{35000}{2100}=16.7\text{min} \end{gathered}$$

$$\begin{gathered} v=201\cdot 1.9=381.9\text{km/h} \\ {t}_2=t\to \text{h}=t:60\text{h}=16.6667:60\text{h}=0.27778\text{h} \\ {s}_2=v\cdot t_2=381.9\cdot 0.2778=\frac{1273}{12}\doteq 106.0833\text{km} \\ {s}_2^2=s_1^2+s^2 \\ s=\sqrt{s_2^2-s_1^2}=\sqrt{106.0833^2-10.668^2}=105.5\text{km} \end{gathered}$$

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