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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.
System: The boat and its contents will be treated as a point particle with an external force from the action of the fan (actually from the air that the fan is pushing).
Model: One-Dimensional Motion With Constant Acceleration
Application:
Immediate effects. Once the fan has been reversed, the acceleration is in the opposite direction from the velocity. Thus, the boat will immediately begin to slow down. As it slows, it will continue to move east. In the language of our one-dimensional system, the velocity immediately begins to decrease with time, but the position continues to increase until the instant that the velocity has decreased to zero.
A warning.
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It is very tempting to assume that as soon as the fan is reversed, the boat begins to move backward. This is not the case, however. Consider the case of a commercial jet landing at over 100 mph. The pilots will usually reverse the engines within a few seconds of landing to help slow the plane. If the plane were to immediately reverse direction, the effect on the passengers would be as if it had hit a brick wall and bounced off! Instead, the plane continues along the runway while gently decreasing its speed. |
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| Info |
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One of the (many) reasons that your intuition might tell you that reversing the engine immediately reverses the direction is experience operating automobiles. In a car, the transmission is not designed to allow you to reverse the engine to slow the car. When the engine is in reverse either the car is moving backward or you are about to spend a few thousand dollars on your transmission. What feature do cars have (that is not present on the air/ice boat) to compensate for the fact that the engine cannot produce a significant acceleration in the direction opposite the car's motion? |
Long-term effects.
The motion is not finished when the boat stops, however. If the fan is left in reverse, the continued thrust will now begin to accelerate the boat backward. In one-dimensional language, the velocity reaches zero and continues to decrease, so the speed (absolute value of velocity) is now increasing. The boat will therefore begin to move west, and with increasing speed. Thus, the position vs. time graph will begin to decrease with a steepening slope.
An important note about constant acceleration.
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B.) Sketch rough graphs of your velocity and position as a function of time from the instant the fan was reversed.
Application: Having already modeled the problem to answer part (A), we present the graphs that illustrate our answer to that part.
Important note: sketching graphs.
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