This is a continuation of a previous question, with more thinking applied, thanks to a helpful comment.

Imagine a glider is airborne in a breezeless sky. The glider is 3 KM high, is traveling at 100 KM / hr, and is descending at a constant rate of 10 m per min. The glider weighs 200 kg. The sole occupant of the glider is a man weighing 100 kg.

Assuming that nothing external to the glider would affect the rate of descent of the glider for a short time (such as a minute), what happens to the glider's altitude or rate of descent if the man jumps in the glider? He jumps straight up (perpendicular to the floor of the glider) to a height of 50 cm and drops back down to the floor. He jumps at the center of mass of the glider and lands in the same spot. Is there any effect to altitude or rate of descent by his muscles pushing off against the floor, and later landing on the floor?

Is there any notable difference from the above action if the man jumps just as before, but as he reaches his maximum height of 50 cm, he grabs on a rope hanging from the ceiling that is attached at the center of the plane? He grabs on tight, instantly transferring his full weight to the rope.

I'm mainly interested in a qualitative answer, but if you wish to produce a formulaic result, of course feel free.

A comment was made suggesting that I consider a system with a trampoline resting on a scale with a man jumping on it. (Thanks to Mike Dunlavey.) Based on your analogy, here are my current thoughts about it.

The weight on the scale with the man at rest is trampoline + man; when he pushes off, the weight would briefly increase by the amount of the force of his push-off, then would briefly be just the weight of the trampoline, and then would be roughly the weight of the trampoline + Man + downward force again.

Applying this to the glider, I believe the effect on the glider would be a small drop in altitude due to the force of the jump. Then while the man is in the air, the now lighter glider would have a slight upward tilt due to it's continued speed, angle of attack of the wing, but temporarily without the man's weight. Then he lands in the glider, and the glider loses some more altitude and its angle tips a bit down too.

I believe the net qualitative result, if the glider were seen from the side and its movement was accurately recorded, would be an interruption in a straight downward line. The first change would be a jog downward, then a small decrease in the slope of the line, then another jog downward and an increase in the slope of the line (making it a bit steeper of a descent).

If the man grabbed the rope after jumping, then his weight would again be acting on the glider, causing a small increase in the downward slope of the plane, but this time only the man's weight and not the additional force of the man dropping by 50 cm would be applied to the glider. So, somewhat less of a downward jog in altitude than in the previous scenario.

Does this reasoning seem sound, and the results approximately correct? Thanks for your help!

  • $\begingroup$ physics.stackexchange.com/questions/56829/… I think the correct way would have been to update the previous question, and flag it for re-opening. $\endgroup$ – Bernhard Mar 16 '13 at 8:36
  • $\begingroup$ Yeah, you're basically right, I think, but don't think of the glider as making sudden changes in descent angle. Rather think of it as experiencing temporary changes in vertical acceleration, giving it short smooth curves down or up, such that the center of mass (man & glider) follows a straight line. $\endgroup$ – Mike Dunlavey Mar 16 '13 at 17:12

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