There is a man attached to a relatively long string with a steel ball
on the other end. This man we will call "Popeye", is strong enough to
lift the ball and throw it up:

1. What's the relation between forces, speed, mass, to make the ball
drag Popeye up thru the air? There are only basic arguments in this
equation, no ellastic string, Popeye's body is not broken, etc...
maybe there is some air drag, if useful.

2. How could Popeye solve how much force he needs to throw his system X meters up?

Now that Popeye is flying, he climbs the string and takes the steel ball:

3. Did Popeye modify the speed of the ball by climbing the string? I
think climbing slower or faster would make different results, but not
sure.

4. Is there a way Popeye can control the direction of his flying
system? How could he do that?

5. Is it possible for Popeye to accelerate his system? How? Would it
help cutting the string?

Regards!

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Clarification of Question by cronodragon-ga on 25 Jul 2005 23:55 PDT

I was thinking, what happens if Popeye changes the steel ball for a
Gyroscope? Would that help in any way to maneuver?

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Request for Question Clarification by richard-ga on 26 Jul 2005 07:40 PDT

If you want a Google Answers Researcher to take this on you should
consider substantially increasing your asking price (there are 7
question marks in your question).  Here is a link to guidelines about
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But I'll note here that the first comment is not correct.  If Popeye
is standing on the earth at the start of the problem, he can launch
the ball and (via the tether) himself into the air.  The equal and
opposite force will be his feet against the earth and the earth
against his feet.

Google Answers Researcher
Richard-ga

Hello,

   This scenario is impossible. As Popeye throws the ball there is
equal force both on the ball, and on Popeye in the exact opposite
direction. They cancel out and the system on average makes no progress
whatsoever. The center of mass stays put.

1. I think you're asking for too much here. The simple answer is the
momentum of the ball will carry him into the air, but adding his mass
to the system (when the tring becomes taut) would decrease the
velocity of the ball.

2. If we can make certain assumptions, for example that he is throwing
the ball straight up and he doesn't move when he throws the ball, then
he gives the ball a certain amount of momentum, p_ball = m_ball *
v_ball. When he lifts off the group as the string because taut, then
his velocity changes, but since the momentum must be conserved (the
total momentum being p_ball, since Popeye was stationary at the
start), we have p_total = m_ball * v_ball + m_Popeye * v_Popeye. We
know m_ball, m_Popeye, and p_total, and we know (since the Popeye is
connected to the ball via a string) that v_ball = v_Popeye. Hence we
can solve for v_Popeye. Then it is simple kinematics to determine how
high he goes (h = v^2 / (2 * g)

3. Nope. Recall, the momentum of Popeye and the ball must be
conserved. Since the momentum equals mass times velocity (p = m * v),
if we know the mass hasn't changed and that the momentum cannot
change, we know the velocity hasn't changed either.

4. If he brought some rocks with him, he could throw them to either
side and thereby change his direction (he would drift in the direction
opposite of the direction he threw the rocks). If we can assume air
resistance, he could utilize that as well (some fins or something).

5. He could, again, by throwing some rocks he brought with him, or
again by using air resistance to help him. If he had really strong
lungs he could blow in a direction and accelerate his system. This
question is basically the same as #4, since acceleration is simply
changing speed and/or direction (recall, acceleration is change in
velocity, and velocity is a speed in a direction). Cutting the string
would do nothing (theoretically speaking).

Hello,

QED100-ga: One assumes that Popeye is standing on the ground, so that
the force applied to him by the ball is cancelled out by the reaction
force from the ground. Therefore it is possible, supposing he can
throw it very very hard.

Eudean-ga's answer is pretty much correct, but a couple of points occur to me: 

(1) and (2) are pretty much the same question, so it puzzles me that
eudean-ga said (1) was too much but gave an outline of how to solve it
in (2).

For (2), we only have to assume he's throwing it straight up to get
the maximum possible height - suppose Popeye applies a force F for a
time t seconds, at an angle of j from the vertical. The momentum
change is Ft, so the initial velocity of the ball is Ft/m_b and
(assuming the string isn't all that long) the initial velocity of both
will be Ft/(m_b + m_p) at angle j. The vertical component of this is
Ft(cos j)/(m_b + m_p) - use this as v in h = v^2/2g to get the height
attained.

To work it backwards as you requested for (2) we get v = sqrt(2gX) and
therefore F = (m_b + m_p).sqrt(2gX) / (t.cos j).

For (4) and (5), as eudean said, once he's launched there's not much
he can do other than throw things out. However, cutting the string
might help - if he climbs onto the ball, then cuts the string, he's
free to jump off the ball which will enable him to change his path
somewhat (he's essentially throwing the ball away rather than extra
rocks as eudean suggested).

"QED100-ga: One assumes that Popeye is standing on the ground, so that
the force applied to him by the ball is cancelled out by the reaction
force from the ground. Therefore it is possible, supposing he can
throw it very very hard."

Keep in mind that if Popeye throws the ball vertically, then he is
recoiled against Earth, and Earth is then pushed away from the ball
and becomes part of the system. For Popeye to literally propell
himself upwards by shoving the ball would mean that the mass center of
the whole system is between Earth & the soles of Popeye's feet. But if
the ball is receeding away due to an impulse, then the mass center
must be between it & Popeye/Earth. Thus, he cannot propell himself in
this fashion. It's impossible.