A student walks 75m Westward and 50m Northbound. What is the student’s displacement?
Understand the Problem
The question is asking for the displacement of a student who walks 75 meters west and 50 meters north. We will calculate the resultant vector using the Pythagorean theorem.
Answer
The displacement of the student is approximately $90.62 \, \text{m}$.
Answer for screen readers
The student's displacement is approximately $90.62 , \text{m}$.
Steps to Solve
- Identify the movements The student walks 75 meters west and 50 meters north. These movements can be considered as sides of a right triangle where:
- One leg (west) = 75 m
- The other leg (north) = 50 m
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Apply the Pythagorean theorem To find the displacement, we will use the Pythagorean theorem, which states: $$ c = \sqrt{a^2 + b^2} $$ where ( c ) is the hypotenuse (displacement), ( a ) is one leg (75 m), and ( b ) is the other leg (50 m).
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Calculate the displacement Plugging in the values: $$ c = \sqrt{(75)^2 + (50)^2} $$ Calculating the squares: $$ c = \sqrt{5625 + 2500} $$ Now, add the squares: $$ c = \sqrt{8125} $$
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Find the square root Now, we calculate the square root: $$ c \approx 90.62 , \text{m} $$
The student's displacement is approximately $90.62 , \text{m}$.
More Information
The displacement represents the shortest distance from the initial to the final position of the student, along with the direction. In this case, it indicates the resultant distance covered by the student moving in two perpendicular directions.
Tips
- Confusing distance with displacement: Distance is the path traveled, while displacement is the straight-line distance from the start to the end point.
- Not using the Pythagorean theorem correctly, especially in identifying the right legs of the triangle.
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