Docking Exercise Preparing for the return to space, NASA needs to train astronauts in spacecraft docking.
Besides simulators, they want to train with actual vehicles, but we have no spacecraft to
use.
That and budget cuts have led to the use of a computer controlled go cart and a semi
tractor trailer with a 5 meter long ramp. In the trailer is a firmly mounted mini docking
ring at the top of the ramp and the go cart has a matching tunnel mounted on the front so
that it will slip into the docking ring and latch. The computer on the go cart has a very
simple set of commands. Each program step specifies a time interval in seconds and either
an acceleration in m/s2 or a velocity in m/s which is to be used for that interval. You can
only specify a velocity to maintain if you are already moving at that velocity. The cart has
sensors which provide distance from the back of the trailer and velocity relative to the
ground and velocity relative to the trailer.
The starting configuration has the cart moving at 5 m/s relative to the road and 200
meters from the bottom of the ramp (205 meters from the docking ring). The truck is
moving at 15 m/s relative to the road. You are to achieve docking within 200 seconds and
the docking clamps need a 0.3 m/s impact speed to set the latches. For safety, your
accelerations should all be less than 5g’s (49 m/s2) and your velocity relative to the truck
should be less than 3 m/s when you are within 15 meters of the ramp (20 meters from
docking).
There is no unique answer for this problem, but do check to make sure that your cart
doesn’t accelerate past the docking ring. A good way to check your solution is to use a
spreadsheet with 1 row per second and calculate the distance to docking at each second.
This isn’t hard, but it does require attention to details and you will likely learn something
about how many variables you can specify without creating a conflict.

Your Solution: velocity in m/s, acceleration in m/s2.