Question

A boat sails 285 miles south and then 132 miles west. What is the magnitude of the boats resultant vector?

Answer 1

The magnitude of the boats resultant vector is 314.1 mi

What is a vector?

A vector is a physical quantity that has both magnitude and direction.

What is a resultant vector?

A resultant vector is the sum of two or more vectors.

How to find the boats resultant vector?

Since the boat sails 285 miles south and then 132 miles west, we have that its first direction vector is r = (285 mi)j. Also, its direction vector west is r' = -(132 mi)i

So, the resultant vector R = r + r'

=  (285 mi)j + (132 mi)i

=  (132 mi)i + (285 mi)j

So, the magnitude of the resultant vector is R = √(r² + r'²)

So, substituting thevalues of the variables into the equation, we have

R = √(r² + r'²)

R = √((285 mi)² + (132 mi)²)

R = √(81225 mi² + 17424 mi²)

R = √(98649 mi²)

R = 314.08 mi

R ≅ 314.1 mi

So, the resultant vector is 314.1 mi

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