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The image you uploaded contains a set of vector-related exercises. I'll go through each problem and provide the solutions:

### Problem 1:
**A ship sails 25 km south then 30 km east. Represent the ship's trail using vector diagram. Find the resultant vector.**

**Solution:**
- The ship's movement can be represented by two vectors:
  - \( \mathbf{A} = 25 \text{ km south} \)
  - \( \mathbf{B} = 30 \text{ km east} \)
  
- These two vectors are perpendicular to each other. The resultant vector \( \mathbf{R} \) can be found using the Pythagorean theorem:

\[
R = \sqrt{A^2 + B^2} = \sqrt{(25)^2 + (30)^2} = \sqrt{625 + 900} = \sqrt{1525} \approx 39.05 \text{ km}
\]

- To find the direction (θ) of the resultant vector:
  
\[
\theta = \tan^{-1}\left(\frac{30}{25}\right) \approx \tan^{-1}(1.2) \approx 50.19^\circ \text{ east of south}
\]

### Problem 2:
**Two forces of 10 N each are acting on a point. One force acts east and the other 70° north of east. Find the resultant vector.**

**Solution:**
- Let the two forces be \( \mathbf{F_1} = 10 \text{ N east} \) and \( \mathbf{

Learn how to solve vector problems involving a ship's trail and forces acting on a point. Includes step-by-step solutions using vector addition and the Pythagorean theorem. Suitable for high school students.

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