triiniityy
Answered

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A boat is traveling at 28 knots in a direction of 36 degrees. It encounters wind moving at 10 knots in a direction of 22 degrees. What is the true velocity and direction of the boat? round to the nearest whole #

a) 38knots;58 degrees
b) 32knots;30 degrees
c) 1,427knots;58 degrees
d) 38knots;32 degrees

Sagot :

facundo3141592

The magnitude of the total velocity of the boat is 38 knots, and the direction is 32°, so the correct option is d.

How to get the velocity of the boat?

First, we need to write need to find the component of the two given velocities.

For the boat, the magnitude is 28 knots and the angle is 36°, then the components are:

  • x-component = (28 knots)*cos(36°) = 22.65 knots
  • y-component = (28 knots)*sin(36°) = 16.46 knots

For the wind, the components are:

  • x-component = (10 knots)*cos(22°) = 9.27 knots
  • y-component = (10 knots)*sin(22°) = 3.75 knots

Adding these, the total components of the boat's velocity are:

  • x-comp =  22.65 knots+ 9.27 knots = 31.92 knots
  • y-comp = 16.46 knots +  3.75 knots = 20.21 knots

Then the magnitude of the velocity is:

|V| = √( (31.92 knots)^2 + (20.21 knots)^2)  =37.78 knots

That can be rounded to 38 knots

To get the angle, we take the arctangent of the quotient between the y-component and the x-component:

a = Atan(20.21 knots/31.92 knots) = 32.34°

Then the correct option is d) 38 knots and 32°

If you want to learn more about velocity, you can read:

https://brainly.com/question/4931057

mayojya

Answer:

It is 38 knots; 32 degrees

Step-by-step explanation:

The answer below is right

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