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Unformatted text preview: Solution for Long-answer Homework 3 Motion problems Solution to Long-answer Homework Problem 3.1(Position/Displacement) Problem: A cruise ship sails from the Bahamas due West at 60 mph. After it sails for 4 hours, it turns around and sails due East for 1 hour and 30 minutes at 45 mph. (a)Write the position vector for the boat, after the first leg of the trip (while its going due West). (b)Write the position vector for the boat, after the second leg (while its going due East). (c)Calculate the displacement vector vectorx for both the second leg of the trip and the entire journey. (d)Calculate the total distance travelled, d . (e)Draw to scale the position vectors for the different legs of the journey. Using the method described in Section 3 . 9 for adding vectors, find both displacement vectors asked for in part (c). Do these results agree with your calculations? Solution to Part (a) Position Vector- First Leg: First we need to define a coordinate system. The easiest system to use is one with the origin at the boats starting point, and the positive x-axis pointing West. For the first leg of the trip, the boat has travelled for 4 hours at 60mph , so the distance it has travelled is (4 hrs ) parenleftbigg 60 miles hr parenrightbigg = 240 miles The position vector is this distance as well as the direction. This vector could be expressed a number of ways, such as 240 miles West or if West were designated as the positive x direction of travel, + 240 miles x . Grading Key: Part (a) 1 Points Solution to Part (b) Position Vector- Second Leg: This position is simply the distance of the first leg minus the distance of the second leg (because the boat is now headed East), so 240- ( 1 . 5 x 45 ) = 240- 67 . 5 = 172 . 5 miles. This vector can again be expressed a number of ways, for ex. 172 . 5 miles West, or 172 . 5 miles x . Grading Key: Part (b) 1 Points Solution to Part (c) (a) Displacement Vector - Second Leg: vectorx Sec.Leg = x f- x i = 172 . 5- 240 =- 67 . 5 miles which means the boat is 67 . 5 miles East of where the second leg began ( East = - West ). (b) Displacement Vector - Entire Trip: vectorx Total = x f- x i = 172 . 5- 0 = 172 . 5 miles West Grading Key: Part (c) 2 Points Solution to Part (d) 1 Total Distance: Total Distance = (Length of First Leg) + (Length of Second Leg) = 240 + 67 . 5 = 307 . 5 miles Grading Key: Part (d) 1 Points Solution to Part (e) Position Vectors: Note that by defining West to be positive, we have a backwards coordinate system. Remember that the way a coordinate system is defined is completely arbitrary. You just have to be consistent once you have defined one. Note also that the position vector after the second leg of the journey is the same vector as the displacement vector for the entire journey, since we defined the starting point to be the origin. This is coincidental, however, as position and displacement are distinct concepts. Make sure you understand the difference between the two.as position and displacement are distinct concepts....
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