Radha walks 14 km towards north. She turns right and walks 22 km. She turns…
2021
Radha walks 14 km towards north. She turns right and walks 22 km. She turns right and walks 24 km. She turns left and walks 26 km. She finally rotates by an angle of 90 degrees in anti-clockwise direction and walks 24 km. How far and in which direction is her starting point from the finishing point?
- A.
50 km, south-west
- B.
76 km, north-west
- C.
76 km, south-east
- D.
50 km, north-west
Attempted by 20 students.
Show answer & explanation
Correct answer: A
Solution:
Start at (0, 0).
Walk 14 km north → position (0, 14).
Turn right (east) and walk 22 km → position (22, 14).
Turn right (south) and walk 24 km → position (22, −10) because 14 − 24 = −10.
Turn left (east) and walk 26 km → position (48, −10) because 22 + 26 = 48.
Rotate 90° anti-clockwise (from east to north) and walk 24 km → final position (48, 14).
Vector from finishing point to starting point = (0 − 48, 0 − 14) = (−48, −14), i.e. 48 km west and 14 km south of the finishing point.
Distance = sqrt(48^2 + 14^2) = sqrt(2304 + 196) = sqrt(2500) = 50 km.
Answer: 50 km, south-west.