Question 9.14: An Airbus 300 is employed in a zero-gravity flight. The flig...
An Airbus 300 is employed in a zero-gravity flight. The flight is started at 8000 m with a velocity of 440 knot and lasts about 20 s. Determine (1) horizontal distance traveled, (2) height lost, (3) vertical velocity, (4) average descent angle and (5) total velocity, at the end of 20 s. Ignore the drag force in the z-direction.
The airspeed of 440 knot is equivalent to 226.3 m/s.
1. Horizontal distance traveled
X=V_ot=226.3\times 20=4527\space m=4.53\space km \quad \quad \quad \quad (9.179)
2. Height lost
\Delta h=\frac{1}{2}gt^2=\frac{1}{2}\times 9.81\times 20^2=1961\space m=1.96 \space km\quad \quad \quad \quad (9.181)
3. Vertical velocity
V_z=\frac{gX}{V_o}=\frac{9.81\times 4527}{226.3}=196.1\space m/s=381.2\space knot\quad \quad \quad \quad (9.180)
4. Average descent angle
\gamma=\tan^{-1}\Big(\frac{h}{X}\Big)=\tan^{-1}\Big(\frac{1961}{4527}\Big)=23.4^{\circ}\quad \quad \quad \quad (9.184)
5. Total velocity
V=\sqrt{V_x^2+V_z^2}=\sqrt{226.3^2+196.1^2}=299.5 \space m/s=1070 \space km/h \quad \quad \quad \quad (9.178)