Question

In an attempt to escape his island, Gilligan builds a raft and sets to sea. The wind shifts a great deal during the day, and he is blown along the following straight lines: 2.50 km 45.045.0^\circ north of west; then 4.70 km 60.060.0^\circ south of east; then 1.30 km 25.025.0^\circ south of west; then 5.10 km straight east; then 1.70 km 5.005.00^\circ east of north; then 7.20 km 55.055.0^\circ south of west; and finally 2.80 km 10.010.0^\circ north of east. What is his final position relative to the island?

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Final Answer

7.34 km, 63.5 S of E7.34 \textrm{ km, } 63.5^\circ \textrm{ S of E}

Solution video

OpenStax College Physics, Chapter 3, Problem 23 (Problems & Exercises)

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Comments

It goes all the way to Vector G not just Vector F

Hello Openstax2021, thank you noticing the issue here. The issue is not that I forgot vector G, but rather than I labeled two different vectors both with the letter E. The final answer is correct, but obviously this creates confusion, and I have flagged the video for a re-do. With the intended vectors A to G, there are 7 vectors. There are 7 terms in the numerical expression for RxR_x, which is correct, although, confusingly, only 6 in the algebraic expression. There are only 6 terms in the expression for RyR_y since vector DD is entirely horizontal. While the final answer is correct, this error obviously needs to be corrected some time.
All the best,
Shaun

This video was updated on Nov. 22nd, 2023