Manoj walks 5 m towards North, then turns to the East and walks 10 m. He turns right and walks 15 m, then turns left and walks 15 m. Which direction is he facing now?
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In direction sense problems, track facing direction after each turn: from East, right→South and left→North; from South, right→West and left→East.
Step 1: Set the starting bearing.
Let North = 0 degrees, East = 90 degrees, South = 180 degrees, and West = 270 degrees. Manoj starts facing North (0 degrees) and walks 5 m.
Step 2: Turn to East.
He turns to face East, so his bearing becomes 90 degrees, and he walks 10 m.
Step 3: Turn right, then turn left.
A right turn adds 90 degrees: \(90 + 90 = 180\) degrees (South), and he walks 15 m facing South. A left turn subtracts 90 degrees: \(180 - 90 = 90\) degrees (East), and he walks 15 m facing East.
Step 4: Final Answer:
After all the turns, Manoj's bearing is 90 degrees, so he ends up facing East.
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Approach Solution -2
Step 1: Build a turn-lookup table.
A right turn always moves the facing one step clockwise through the cycle North to East to South to West and back to North. A left turn always moves it one step counter-clockwise through the same cycle: North to West to South to East and back to North.
Step 2: Track Manoj's facing using only this table.
He starts facing North and walks 5 m, facing unchanged. He then turns to face East directly (given in the question) and walks 10 m.
Step 3: Apply the table for the remaining two turns.
He turns right from East: in the clockwise cycle North-East-South-West, the step after East is South, so he now faces South and walks 15 m. He then turns left from South: in the counter-clockwise cycle North-West-South-East, the step after South is East, so he now faces East and walks 15 m.
Step 4: Final Answer:
Following the turn cycle through both turns, right from East to South, then left from South to East, Manoj ends up facing East.
