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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 $45.0^\circ$ north of west; then 4.70 km $60.0^\circ$ south of east; then 1.30 km $25.0^\circ$ south of west; then 5.10 km straight east; then 1.70 km $5.00^\circ$ east of north; then 7.20 km $55.0^\circ$ south of west; and finally 2.80 km $10.0^\circ$ north of east. What is his final position relative to the island?

$7.34 \textrm{ km, } 63.5^\circ \textrm{ S of E}$

Note: while the final answer is correct, there is confusion in the video owing to the fact that I mistakenly labeled two vectors both $E$. There should be 7 vectors labeled $A$ to $G$. The numerical work is correct in that there are 7 terms in the expression for $R_x$. There are only 6 terms in the expression for $R_y$ since vector $D$ has no vertical component. This video has been flagged for a re-do.

Solution Video

# OpenStax College Physics Solution, Chapter 3, Problem 23 (Problems & Exercises) (8:56)

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Submitted by Openstax2021 on Tue, 02/09/2021 - 12:26

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

Submitted by ShaunDychko on Wed, 02/10/2021 - 11:16

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 $R_x$, which is correct, although, confusingly, only 6 in the algebraic expression. There are only 6 terms in the expression for $R_y$ since vector $D$ is entirely horizontal. While the final answer is correct, this error obviously needs to be corrected some time.
All the best,
Shaun