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
