Ritu leaves her gate facing North and covers 15 m. At the first corner she takes a right and covers 20 m; at the next corner, a right again and 30 m; then a left and 10 m; then a left and 35 m; and at the last corner, a left and 15 m. How far and in which direction is she now from her gate?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 25 m North-East
A right turn moves the facing direction one step clockwise (North → East → South) and a left turn one step anticlockwise (South → East → North → West). Track the facing direction after every turn and keep a running total of the distance from the gate.
Facing North, 15 m: 15 m north of the gate
Turns right, now facing East, 20 m: 15 m north, 20 m east
Turns right, now facing South, 30 m: \(30-15=15\) m south, 20 m east
Turns left, now facing East, 10 m: 15 m south, \(20+10=30\) m east
Turns left, now facing North, 35 m: \(35-15=20\) m north, 30 m east
Turns left, now facing West, 15 m: 20 m north, \(30-15=15\) m east
Distance \(=\sqrt{15^{2}+20^{2}}=\sqrt{225+400}=\sqrt{625}=25\) m
She is north and east of the gate, so the direction is North-East
Ritu is 25 m North-East of her gate.
