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The elves have recovered the wrecked sled and
most of the debris they could find. They have also rather
successfully attempted to restore the crash site. The black box was
not retrieved however, and the technical investigation is halted in
its absence.
With christmas coming closer the elves have no time to spare to
search for it themselves as they already have to work overtime in
the workshop to finish making all the toys and compiling the lists
of who has been naughty and who has been nice. They now need your
help to locate the box as soon as possble so the investigation can
finish and the sleds be allowed to fly again before it is too
late.
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The coordinate system used by the elves is not
very useful if you are not an elf, as it is made for navigation at
extreme velocities and is centered at a point where the only
direction is south. The preliminary report from the crash does
contain information on what manuevers were executed before the
crash, perhaps you can calculate where the sled struck ground from
that?
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The testing sequence started with a visual
inspection and some basic technical tests on the ground which the
sled passed with flying colors. It was then towed over to the
runway where it, after a few final checks, received clearance for
take-off. The sled accelerated along the runway at a bearing of
316° with a constant acceleration of 56ms-2 for 2s,
followed by a climb at constant speed at a 24° angle.
So far it was a flawless routine take-off, but 12 seconds into
the climb there was a partial break of the thill forcing the sled
to turn left at 17°/s.
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At this point the climb was immediately halted
and an emergency plan involving following the turn around at
constant height followed by an attempt to break the turn and land
on the runway was carried out. This attempt failed however, as the
thill broke completely 8s into the turn after which the sled had a
ballistic free-fall.
As Santa's sleds are built to deliver billions of presents all
over the world in just a few hours they are by necessity not
affected by drag or wind, nor will they drift during turns. For
your calculations it may also be useful to know that minor turns
are instantaneous, the world is perfectly flat, one arc minute of
latitude is 1852 meters, one arc minute of longitude is 1852*cos59°
meters and g=9.82ms-2. Do not round any numbers during
your calculations.
No elves were harmed during the creation of this
cache.
