An ant moves 10 cm towards the East and turns to its right, moving 3 cm. It…
2024
An ant moves 10 cm towards the East and turns to its right, moving 3 cm. It then turns to its right again and moves 3 cm. Next, it turns to its left and moves 2 cm. Finally, it turns to its right and travels 7 cm. How far and in which direction is it now from the starting point?
- A.
3 cm East
- B.
5 cm South
- C.
7 cm West
- D.
5 cm North
Show answer & explanation
Correct answer: B
Concept: In a direction-test problem, a right turn rotates the facing direction one step clockwise (North -> East -> South -> West -> North) and a left turn rotates it one step anticlockwise. Resolve every leg onto two perpendicular axes — East-West and North-South — and sum each axis separately; the net displacement from the start is given by those two totals combined.
Start facing East and move 10 cm East. Running position: 10 cm East.
Turn right from East, so now facing South; move 3 cm South. Running position: 10 cm East, 3 cm South.
Turn right from South, so now facing West; move 3 cm West. Running position: 7 cm East, 3 cm South.
Turn left from West, so now facing South; move 2 cm South. Running position: 7 cm East, 5 cm South.
Turn right from South, so now facing West; move 7 cm West. Running position: 0 cm East, 5 cm South.
Net East-West displacement: the 7 cm East cancels exactly against the 7 cm West, leaving 0. Net North-South displacement: 5 cm South, with nothing to offset it.
Cross-check: the two westward legs together (3 cm + 7 cm = 10 cm West) exactly cancel the single 10 cm eastward leg, confirming the horizontal axis nets to zero; the two southward legs together (3 cm + 2 cm = 5 cm South) have no northward leg to balance them, confirming the full vertical displacement.
Final position: 5 cm South of the starting point.