A car drives 50 meters at 45° north of east. Resolve the displacement into its northward and
eastward components. (35.36 m, N; 35.36 m, E)

To resolve the displacement of the car into its northward and eastward components, we need to break the displacement vector into two perpendicular components using trigonometric functions. Given:

- Displacement magnitude, \( d = 50 \) meters
- Direction, \( \theta = 45^\circ \) north of east

### Components of displacement:
1. **Eastward Component**: 
   - This is the horizontal (x-axis) component.
   - \( d_{\text{East}} = d \cdot \cos(\theta) \)
   
2. **Northward Component**: 
   - This is the vertical (y-axis) component.
   - \( d_{\text{North}} = d \cdot \sin(\theta) \)

Since \( \theta = 45^\circ \) and \( d = 50 \) m, the calculations are as follows:

### Eastward Component:
\[
d_{\text{East}} = 50 \cdot \cos(45^\circ) = 50 \cdot \frac{1}{\sqrt{2}} \approx 35.36 \, \text{meters}
\]

### Northward Component:
\[
d_{\text{North}} = 50 \cdot \sin(45^\circ) = 50 \cdot \frac{1}{\sqrt{2}} \approx 35.36 \, \text{meters}
\]

Thus, the displacement components are approximately:
- **Northward component**: \( 35.36 \, \text{meters} \)
- **Eastward component**: \( 35.36 \, \text{meters} \)

Both components are equal because the angle is \( 45^\circ \), making the triangle isosceles.

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Would you like further clarification or additional details on this? Here are five related questions to deepen your understanding:

1. How would the displacement components change if the angle were \( 30^\circ \) instead of \( 45^\circ \)?
2. What are the units of displacement, and why are they important in vector resolution?
3. How would you calculate the total displacement if the components were known first?
4. How do you resolve a vector in 3D space, such as if the car was moving upwards as well?
5. What would be the displacement components if the car traveled south of west instead?

**Tip**: Always remember to check if the angle is measured from the horizontal (East-West) axis when resolving vectors.

A car drives 50 meters at 45° north of east. Resolve the displacement into its northward and eastward components. (35.36 m, N; 35.36 m, E)

Resolve a 50-meter displacement at 45° north of east into its northward and eastward components. Using trigonometric functions, learn how to calculate the displacement components of 35.36 meters each. Ideal for high school students learning about vector resolution and trigonometry.

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