Q1.11 Three archers each fire four arrows at a target. Joe's four arrows hit at points 10 cm above, 10 cm below, 10 cm to the left and 10 cm to the right of the center of the target. All four of Moe's arrows hit within 1 cm of a point 20 cm from the center, and Flo's four arrows all hit within 1 cm of the center. The contest judge says that one of the archers is precise but not accurate, another archer is accurate but not precise, and the third archer is both accurate and precise. Which description goes with which archer? Explain your reasoning.
Response: Joe is accurate but not precise (the average position of his arrows are in the bullseye, but none of the arrows are close together), Moe is precise but not accurate (all of his arrows are grouped closely together, but none are close to the bullseye), and Flo is both accurate and precise. Matt Parker has a great video explaining the difference.
Q1.12 A circular racetrack has a radius of 500 m. What is the displacement of a bicyclist when she travels around the track from the north side to the south side? When she makes one complete circle around the track? Explain your reasoning.
Response: The cyclists displacement from the northernmost point to another point on the circle is 1000 m ⋅ cos(θ), where θ is the angle formed by diameter through the north and south points on the circle (radius = 500 m, so the diameter = 1000 m) and the straight line from the northernmost point to the cyclist's current point on the circle. Note that θ must be between 0 and 90 degrees. The displacement is smallest at 90 degrees and greatest a 0 degrees. When the cyclist travels all the way around the track, the displacement is equal to zero.
Q1.13 Can you find two vectors with different lengths that have a vector sum of zero? What length restrictions are required for three vectors to have a vector sum of zero? Explain your reasoning.
Response: The sum of two vectors is zero if the two vector's magnitudes are equal. The sum of three arbitrary vectors A, B, and C if A + B = -C.
Q1.14 One sometimes speaks of the "direction of time" as evolving from past to future. Does this mean that time is a vector quantity? Explain your reasoning.
Response: My instinct is that time is not a vector quantity. There is certainly a magnitude component, but since there is only one possible direction for time to proceed into, the direction aspect seems unnecessary/redundant. Therefore, my conclusion is that time is a scalar quantity, not a vector quantity.
Q1.15 Air traffic controllers give directions to airline pilots telling them in which direction they are to fly. These instructions are called "vectors" If these are the only instructions given, is the name "vector" used correctly? Why or why not?
Response: If these are the only instructions given, they are not true vectors because vectors must have both a magnitude and a direction. These instructions lack a magnitude (how far does the pilot need to fly)?
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ReplyDeletethanks a lot it adds ideas to me
ReplyDelete1. A racetrack forms a circle has a diameter of 1000 m. What is the displacement of a bicyclist when she travels around the track from the north side to the south side? When she makes one complete circle around the track?
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