Question

Sammy squirrel is steering his boat at a heading of 310 degrees at 5mph. The current is flowing at 2mph at a heading of 110 degrees. Find Sammy's course.​

Answer 1

Sammy's course is 3.19 mph at a heading of 322.36°

Explanation:

To solve this problem we need to calculate a sum of vectors.

We can calculate this sum decomposing both vectors in their horizontal and vertical component, and then we sum the components:

First vector: module 5, direction 310°

`horizontal\ component: 5 * cos(310) = 3.2139`

`vertical\ component: 5 * sin(310) = -3.8302`

Second vector: module 2, direction 110°

`horizontal\ component: 2 * cos(110) = -0.6840`

`vertical\ component: 2 * sin(110) = 1.8794`

Resultant vector:

`horizontal\ component: 3.2139 - 0.6840 = 2.5299`

`vertical\ component: -3.8302 + 1.8794 = -1.9508`

Now, to go back to the polar form, we can use the following procedure:

`module = √(horizontal\ component^2 + vertical\ component^2 )`

`module = √(2.5299^2 + (-1.9508)^2 )`

`module = 3.1947`

`angle = arc tangent(vertical\ component / horizontal\ component)`

`angle = arc tangent(-1.9508 / 2.5299)`

`angle = 322.36\°`

So Sammy's course is 3.19 mph at a heading of 322.36°