Question

Sammy squirrel is steering his boat at a heading of 327 degree at 18mph. The current is flowing at 4mph at a heading of 60 degrees. Find Sammy's course.​

Answer 1

• 59.97 º at 18.23 mph

Step-by-step explanation:

To find Sammy's course you have to add the two velocities (vectors), 18 mph 327º and 4 mph 60º.

To add the two vectors analytically you decompose each vector into their vertical and horizontal components.

1. 18 mph 327º

• Horizontal component: 18 mph × cos (327º) = 15.10 mph

• Vertical component: 18 mph × sin (327º) = - 9.80 mph

• Vector notation:

`15.10\hat i-9.80\hat j`

2. 4 mph 60º

• Horizontal component: 4 mph × cos (60º) = 2.00 mph

• Vertical component: 4 mph × sin (60º) = 3.46 mph

• Vector notation:

`2.00\hat i+3.46\hat j`

3. Addition:

You add the corresponding components:

`15.10\hat i-9.80\hat j+2.00\hat i+3.46\hat j\\ \\ 17.10\hat i-6.34\hat j`

To find the magnitude use Pythagorean theorem:

• 
  `√(17.1^2+6.34^2)= 18.23`

4. Direction:

Use the tangent ratio:

• 
  `tan(\alpha )=opposite/adjacent=3.46/2.00=1.73`

Find the inverse:

• arctan (1.73) ≈ 59.97º