In microgravity astronaut training and equipment testing, NASA flies a KC135A ai

Question

In microgravity astronaut training and equipment testing, NASA flies a KC135A aircraft along a parabolic flight path. As shown in the figure, the aircraft climbs from 24,000 ft to 29,450 ft, where it enters a parabola with a velocity of 136 m/s at 45.0° nose high and exits with velocity 136 m/s at 45.0° nose low. During this portion of the flight, the aircraft and objects inside its padded cabin are in free-fall; astronauts and equipment float freely as if there were no gravity.

(b) What is the aircraft's altitude at the top of the maneuver?
________ ft

(c) What is the time spent in zero gravity?
________ s

Explanation / Answer

During the ballistic flight, the aircraft moves under the sole influence of earth's gravity, just like a projectile.
The components of its velocity when entering the zero-g flight are
vx = 136cos45 = 97 m/s
vy = 136sin 45 = 97 m/s
and at the end of the parabolic flight path are
v'x = 136 cos(-45) = 97 m/s
v'y = 136 sin (-45) =-97 m/s
In what follows I neglect the change of g in function of altitude and assume that it is always 9.8 m/s²

The velocity of the aircraft at the top of the maneuver is the same as its horzontal component vx, that is 97m/s

(b) The height it climbs:
y = (0 - vy²)/2a = - (97²)/2×(9.8) = 480 m
The altitude of the top of the flight path
y = y0 + y = 29,450 ft + 480 m = 8976 m + 480 m = 9,456 m

(c) The time interval spent in zero-g
t = (vy)/a = (v'y - vy)/-g = -194/-9.8
t = 19.79 s

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