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A cruise ship is traveling northwest so that it makes a 45-degree angle with the east-west line. If it has traveled 35 miles from its starting point, what are the components of the vector s formed by the ship's path?

User Andy Sander
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2 Answers

14 votes
14 votes

Answer:

Explanation:

A cruise ship is traveling northwest so that it makes a 45-degree angle with the east-example-1
User Jeff Gortmaker
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2.9k points
14 votes
14 votes

Answer:

(17.5√2 miles west, 17.5√2 miles north)

Explanation:

The distance in the west direction will be ...

35cos(45°) = 17.5√2 . . . . miles west

The distance in the north direction will be ...

35sin(45°) = 17.5√2 . . . . miles north

The vector components are ...

(17.5√2 miles west, 17.5√2 miles north)

_____

Additional comment

When a map with the usual "north is up" orientation is overlaid on an x-y coordinate grid, the (x, y) ordered pair directions correspond to (east, north). Using that coordinate meaning for the vector components here, they would be ...

(-24.7, 24.7) miles

User Eriola
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