Math Problem Statement
A boy runs 4 km to the East side then turns to the right side 6 km, and then turns left runs 8 km again. Turn left to run 3 km again, turn left 4 km, then turn right 1 km. Now the boy is in which direction?
Solution
Let's break down the boy's movements step by step and determine his final position and direction:
- First Movement: The boy runs 4 km to the East.
- Second Movement: The boy turns right (which is towards the South) and runs 6 km.
- Third Movement: The boy turns left (which is towards the East again) and runs 8 km.
- Fourth Movement: The boy turns left (which is now towards the North) and runs 3 km.
- Fifth Movement: The boy turns left (which is towards the West) and runs 4 km.
- Sixth Movement: The boy turns right (which is towards the North) and runs 1 km.
Final Direction:
After these steps, the boy is now facing North.
Would you like a detailed breakdown of his final position or any other clarification?
Here are 5 related questions to expand your understanding:
- How would the boy's final position change if he turned right instead of left on his third turn?
- What would the total distance traveled by the boy be?
- How could you represent this motion on a coordinate plane?
- What if the boy turned left after every move; where would he end up?
- How would this problem change if the directions were given as bearings (angles)?
Tip: Always keep track of direction changes as turning left or right alters relative orientation.
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Math Problem Analysis
Mathematical Concepts
Geometry
Direction and Movement
Coordinate System
Formulas
-
Theorems
Pythagorean Theorem (optional if discussing distance)
Right-hand rule for turns and direction
Suitable Grade Level
Grades 6-8
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