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s344n2d4d5 [400]
3 years ago
9

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 degre

es. Find Sammy's course.​
Physics
1 answer:
Tanya [424]3 years ago
5 0

Answer:

  • 59.97 º at 18.23 mph

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.

<u>1. 18 mph 327º</u>

  • 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

<u>2. 4 mph 60º</u>

  • 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

<u>3. Addition:</u>

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:

  • \sqrt{17.1^2+6.34^2}= 18.23

<u>4. Direction:</u>

Use the tangent ratio:

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

Find the inverse:

  • arctan (1.73) ≈ 59.97º
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