Mr. Yorly starts from Point A and drives 16 km towards South. He then takes a right turn, drives 14 km, turns right and drives 44 km. He then takes a right turn and drives 2 km, turns right drives 15 km. He then takes a left turn drives 21 km. He takes a final right turn, drives 13 km and stops at Point P. How far (shortest distance) and towards which direction should he drive in order to reach Point A again? (All turns are 90 degrees turns only unless specified.)
9 km to the West
Take A as origin with East as +x and North as +y, and track the facing direction after each 90° turn.
Drive 16 km South (facing S): position (0, −16).
Right turn (S → W), drive 14 km: position (−14, −16).
Turn right (W → N), drive 44 km: position (−14, 28).
Right turn (N → E), drive 2 km: position (−12, 28).
Turn right (E → S), drive 15 km: position (−12, 13).
Left turn (S → E), drive 21 km: position (9, 13).
Final right turn (E → S), drive 13 km: position (9, 0). This is Point P.
P is at (9, 0) and A is at (0, 0): same y, so P is due East of A by 9 km. To return to A he must drive 9 km towards the West.
Hence the shortest distance is 9 km to the West.
Similar Questions
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- Read the given paragraph carefully and answer the question.
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What is the distance covered by Ram to reach shop A from his home? - John and Jenny stood at a point facing the north. John left Jenny in the morning and walked towards the west for 3 km, taking 15 minutes. Then he moved towards the south for 4 km, taking 25 minutes. What is the shortest distance Jenny needs to travel to meet John?
Important Questions from Direction and Distance
- Vijendra walks a certain distance, say X metres, from his home towards the west. Then he turns left and walks 23 metres. After that, he turns left and walks 36 metres. Then he turns left again to walk 23 metres. He finally turns left and walks 18 metres to reach his home. Find the value of X.
Gaurav exits from the backdoor of his north-facing house and walks 25 m straight, then he takes a left turn and walks 36 m, then he turns left and walks 47 m. He turns left again and walks 36 m. How far and in which direction is he from his house now?
Reeta is standing facing south-east. First, she turns 135° clockwise. After that, she turns 90 ° anticlockwise. Then she turns 45 ° clockwise, followed by a 135 ° anticlockwise turn. In which direction is she facing now?
Sahasra started running from her house towards the north. After 40 meters she turned left and ran for 75 meters. She then turned right and ran for 30 meters, and again turned right to run 75 meters. In which direction was she running finally?
At the time of sunset, Lopa and Kritika are sitting facing each other. If the shadow of Lopa falls to the right of Kritika, in which direction is Kritika facing?
