Pictured here is the University of Manitoba Center for Earth Observation Science's air/ice boat "Skippy". Skippy has a large fan at the back to allow it to accelerate as it slides across icy surfaces. Suppose you are piloting a similar craft on very slippery ice which will not slow your craft at all. Suppose also that the fan on your craft can be reversed instantanously, switching its direction of thrust from forward to backward. Assume the action of the fan (when it is on) always produces an acceleration with the same constant magnitude. Air resistance is negligible.
For the questions in this example, use the following coordinate system. You have a Base Camp at position x=0. Your group's assignment is to make observations of ice thickness at two stations. Station One is 1 mile east of Base Camp, and Station Two is 2 miles west of Base Camp. Take east to be the positive x-direction.
Part 1
A.) Suppose you have left Base Camp and are halfway to Station One. You have been accelerating to the east the entire trip, but you now realize you have forgotten your gloves. You immediately flip the fan control switch to backward, reversing the direction of the thrust. Describe in words what will happen to your position and your velocity from the instant you reversed the fan.
B.) Sketch rough graphs of your position and velocity as a function of time from the instant the fan was reversed.
C.) Given that the boat was halfway to Station One before you reversed it, that it started from rest at Base Camp, and that the fan was accelerating the boat forward until the instant you reversed it, where will the boat be when it (instantaneously) comes to rest after you have reversed the fan?
D.) Suppose that once you have reversed the fan, you keep the fan reversed and on. Will you arrive safely back at Base Camp?
Part 2
Suppose you are making your daily rounds. This involves:
- starting from rest at the Base Camp
- traveling to Station Two
- remaining at Station Two for the same amount of time it took to get there
- turning the boat around and traveling to Station One (without stopping at Base Camp)
- remaining at Station One for the same amount of time you were at Station Two
- turning the boat around and returning to Base Camp and stopping there
A.) Plot graphs of your position and velocity as a function of time for your entire daily rounds.
B.) Divide your graphs into segments and label each segment with the direction of the fan switch (forward or backward) during that segment.