Math Problem Statement
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)
Solution
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, meters
- Direction, north of east
Components of displacement:
-
Eastward Component:
- This is the horizontal (x-axis) component.
-
Northward Component:
- This is the vertical (y-axis) component.
Since and m, the calculations are as follows:
Eastward Component:
Northward Component:
Thus, the displacement components are approximately:
- Northward component:
- Eastward component:
Both components are equal because the angle is , making the triangle isosceles.
Would you like further clarification or additional details on this? Here are five related questions to deepen your understanding:
- How would the displacement components change if the angle were instead of ?
- What are the units of displacement, and why are they important in vector resolution?
- How would you calculate the total displacement if the components were known first?
- How do you resolve a vector in 3D space, such as if the car was moving upwards as well?
- 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.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Vector Resolution
Trigonometry
2D Displacement
Formulas
Eastward Component: d_East = d * cos(θ)
Northward Component: d_North = d * sin(θ)
Theorems
Pythagorean Theorem (for resolving vectors)
Suitable Grade Level
Grades 9-12
Related Recommendation
Find the X-Component of a Vector with 35 N at 55° North of East
Calculate Resultant Displacement Using Vector Components and Trigonometry
Calculating Total Displacement and Comparing it with Distance Traveled
Find the Direction of a Hiker's Resultant Displacement Using Trigonometry
Calculating Eastward Displacement Component Using Trigonometry