My problem is when i use one approach for a question (such as the second approach on the first question) i get an incorrect answer and vise versa

Umm. If done correctly, the same approach should be okay.

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A yacht is sailing at a speed of 34 knots and a wind encounters from the south east, find the final speed and direction of the yacht..

The problem is not complete. Which direction is the yacht sailing.

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But i also get these questions and they require a different approach to solve:

A yacht is moving 10kmph in a south easterly direction and encounters a 3 kmph current from the north. Find the actual speed and direction of the yacht.

...this question requires a different approach to solve using vectors which involves finding the vector in component form and adding the coordinates, then finding the scalar product to find the answer for the speed...

The approach can be the same. You solve for the horizontal and vertical components of the vectors by using sine or cosine.

"south easterly" means the vector's direction is 45degrees south of east.

"from the north" means the vector's direction is vertically downward, or 90degrees south of east.

So collect all easterly components,

E = 10cos(45deg) +3cos(90deg)

E = 7.071 +0

E = 7.071 kph

And collect the southerly components,

S = 10sin(45deg) +3sin(90deg)

S = 7.071 +3

S = 10.071 kph

So, speed = sqrt(E^2 +S^2)

speed = sqrt[(7.071)^2 +(10.071)^2]

speed = sqrt(151.424)

speed = 12.305 kph ---------------answer.

And, direction of the yacht:

Based from the south axis,

tan(theta) = E/S = 7.071 /10.071 = 0.702

theta = arctan(0.702) = 35 degrees

Therefore, the yacht is actually sailing in the (South 35degrees East) direction. ---answer.