Vectors and Projectiles - Mission VP3 Detailed Help

Two vectors with a magnitude of 5 units and 8 units (or 12 units) are being added. The resultant vector could have a magnitude that ranges from ...

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Minds on Physics is a minds-on activity. The part of the mind used most often is the processor, not the memory (to use computer science jargon). If you are having difficulty with this question, avoid trying to recall a fact from memory. Instead, give the question considerable thought. An impulsive answer is often a wrong answer. Rather than be impulsive, take the time to read and be informed. Take some additional time to reflect and think. Use the audio file (Tune In! Listen!), the strategy discussed in the Game Plan section, or the first link in the Hot Link section to a very informative animation. An informed and thoughtful answer is always a better alternative to an impulsive answer.

A useful strategy is to simply construct several sketches of the addition of two vectors with magnitude of 5 and 8.
  • Start by drawing the 5 unit vector to the east. Then add the 8 units to it in the same direction. What is the resultant? Can you ever add the 5 and the 8 to get the resultant to be larger than this?
  • Now begin to redraw the 5 + 8, keeping the 5 unit vector oriented eastward, but rotating the 8 units about 45 degrees counterclockwise (CCW). What is happening to the magnitude of the resultant? Is it getting bigger or smaller?
  • Keep redrawing the addition of 5 + 8 with the 5 unit vector maintaining the east direction and the 8 unit continually rotating CCW. Draw the resultant and keep asking if the magnitude has reached a minimum value. You are looking for the two orientations of the 8 unit vector which will lead to the maximum resultant and to the minimum resultant.