A vector of magnitude 13 makes an angle ` 65.37^(@)` with the x-axis . What is its component along positive y-axis ?

Answer

To find the component of a vector along the positive y-axis, we can use the following steps:

### Step 1: Identify the given values
- Magnitude of the vector (R) = 13
- Angle with the x-axis (θ) = 65.37°

### Step 2: Use the formula for the vertical component
The vertical component (Vy) of the vector can be calculated using the formula:
\[ Vy = R \cdot \sin(\theta) \]

### Step 3: Substitute the values into the formula
Now, substituting the values we have:
\[ Vy = 13 \cdot \sin(65.37°) \]

### Step 4: Calculate the sine of the angle
Using a calculator or trigonometric tables, we find:
\[ \sin(65.37°) \approx 0.91 \]

### Step 5: Calculate the vertical component
Now, substituting the sine value back into the equation:
\[ Vy = 13 \cdot 0.91 \]
\[ Vy \approx 11.83 \]

### Final Answer
The component of the vector along the positive y-axis is approximately **11.83**.

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