
An ostrich is running at a speed of 17.0 m/s in a direction of 68.0° north of west.  What is the magnitude of the ostrichs velocity components?

To find the magnitude of the velocity components of the ostrich running at 17.0 m/s in a direction of 68.0° north of west, we can decompose the velocity vector into its horizontal (west-east) and vertical (north-south) components using trigonometric functions.

### Step 1: Define the Components
- Let \( v \) be the velocity of the ostrich: \( v = 17.0 \, \text{m/s} \).
- The angle given is \( 68.0^\circ \) north of west.

### Step 2: Find the Components
1. **West (horizontal) component, \( v_x \)**:
   Since the direction is north of west, this component is along the west direction (negative x-axis):
   \[
   v_x = v \cdot \cos(68.0^\circ)
   \]

2. **North (vertical) component, \( v_y \)**:
   This component is along the north direction (positive y-axis):
   \[
   v_y = v \cdot \sin(68.0^\circ)
   \]

### Step 3: Calculate the Components
Let's calculate the numerical values of these components.The magnitude of the ostrich's velocity components are:

1. West (horizontal) component, \( v_x \approx 6.37 \, \text{m/s} \).
2. North (vertical) component, \( v_y \approx 15.76 \, \text{m/s} \).

Would you like to explore further details or have any questions?

Here are some related questions to expand your understanding:
1. How would the velocity components change if the direction was south of west?
2. What would be the effect of increasing the speed on the components?
3. How do you determine the direction from given velocity components?
4. What trigonometric identities are used in calculating vector components?
5. How can you find the resultant vector from its components?

**Tip:** Always use the correct sign for direction when working with components, as it indicates the direction on a coordinate plane.

Explore how to find the magnitude of velocity components of an ostrich running at 17.0 m/s in a direction 68.0° north of west. Learn the formulas and step-by-step calculations involving vectors and trigonometry. Suitable for students in Grades 11-12.

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