Matt is attempting to sail a sailboat northeast across the river with a velocity of 13 m/s relative to the

current of water. The water current is flowing from south to north at a velocity of 6 m/s. If the angle between
the velocity of the sailboat and the water current is 40 degrees
, what is the resultant or true velocity of the sailboat?

N component ... 6 m/s + 13cos(40º) m/s

E component ... 13sin(40º) m/s

(resultant)^2 = N^2 + E^2

N component ... 6 m/s + 13cos(40º) m/s

E component ... 13sin(40º) m/s

(resultant)^2 = N^2 + E^2

tan(direction) = N / E

Hey thanks, but could you explain it a little? But also would the final resultant be 13sin(40)m/s? Why would we not use cos in this instant?

Actually I think I got it. So I could just add both N component and E component together to get a final resultant of 22.911 N of E then correct? Thanks

To find the resultant or true velocity of the sailboat, you can use vector addition. Here's how you can solve the problem step by step:

1. Draw a diagram: Draw a diagram representing the river with the current flowing from south to north. Mark the velocity vectors for both the sailboat and the water current. Also, label the angle between the velocity of the sailboat and the water current as 40 degrees.

2. Resolve the vectors: Since we want to find the resultant velocity, we need to break down the given velocities into their horizontal and vertical components.

- Sailboat's velocity: The given velocity of the sailboat relative to the current (13 m/s) can be resolved into horizontal and vertical components using trigonometry. The horizontal component is given by 13 * cos(40°), and the vertical component is given by 13 * sin(40°).

- Water current's velocity: The velocity of the water current is flowing directly from south to north, so its horizontal component is 0 m/s, and the vertical component is 6 m/s.

3. Add the horizontal components: To get the resultant horizontal velocity, simply add the horizontal components of the sailboat's velocity and the water current's velocity.

Resultant horizontal velocity = Sailboat's horizontal component + Water current's horizontal component
Resultant horizontal velocity = 13 * cos(40°) + 0

4. Add the vertical components: To get the resultant vertical velocity, add the vertical components of the sailboat's velocity and the water current's velocity.

Resultant vertical velocity = Sailboat's vertical component + Water current's vertical component
Resultant vertical velocity = 13 * sin(40°) + 6

5. Calculate the resultant velocity: To find the magnitude of the resultant velocity, use the Pythagorean theorem.

Resultant velocity = sqrt(Resultant horizontal velocity^2 + Resultant vertical velocity^2)

6. Round the resultant velocity to the desired precision, if necessary.

So, by following these steps, you can find the resultant or true velocity of the sailboat.