A child runs 25 feet towards north, then he turns towards right and walks 40…
A child runs 25 feet towards north, then he turns towards right and walks 40 feet. Again he turns right and walks 45 feet. Then he turns left and walks 20 feet. Finally he turns right and walks 20 feet. The child is in which direction from his starting point?
Answer: D. South - East — In a direction-sense (distance and direction) problem, plot each leg of the journey along two perpendicular axes - North-South and East-West - starting from…
- A.
North
- B.
South
- C.
South - West
- D.
South - East
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Correct answer: D
In a direction-sense (distance and direction) problem, plot each leg of the journey along two perpendicular axes - North-South and East-West - starting from the origin. Apply the compass rule for each turn (facing a direction, a right turn rotates 90° clockwise and a left turn rotates 90° counter-clockwise), then combine the net north-south and east-west displacements into a single resultant direction.
Start at the origin (0, 0), facing north.
Walk 25 feet north to reach (0, 25).
Turn right (now facing east) and walk 40 feet to reach (40, 25).
Turn right again (now facing south) and walk 45 feet to reach (40, -20).
Turn left (now facing east) and walk 20 feet to reach (60, -20).
Turn right (now facing south) and walk 20 feet to reach (60, -40).
The child's final position is 60 feet east and 40 feet south of the starting point, so the child is in the south-east direction from the start.
Cross-check: total northward distance is 25 feet, and total southward distance is 45 + 20 = 65 feet, giving a net of 65 - 25 = 40 feet south. Total eastward distance is 40 + 20 = 60 feet with no westward movement, giving a net of 60 feet east. Both the south and east components are non-zero, confirming the south-east direction.