Harshad started from his school and moved 100 m towards East and then turned…
2023
Harshad started from his school and moved 100 m towards East and then turned left and moved 200 m and reached a shop. From the shop he moved 200 m towards West and turned to his left and moved 500 m and finally, turned to his left and moved 100 m to reach his home. What is the direction and shortest distance of his home from school?
- A.
South, 300 m
- B.
North, 300 m
- C.
North, 200 m
- D.
East, 250 m
Attempted by 190 students.
Show answer & explanation
Correct answer: A
Solution: Compute the net displacement by tracking each move from the school. Take east as the positive x-direction and north as the positive y-direction.
Start at school: (0, 0).
Move 100 m East → position becomes (100, 0).
Turn left (facing East, left is North) and move 200 m → position becomes (100, 200).
From the shop, move 200 m West → position becomes (100 - 200, 200) = (-100, 200).
Turn left (facing West, left is South) and move 500 m → position becomes (-100, 200 - 500) = (-100, -300).
Finally turn left (facing South, left is East) and move 100 m → position becomes (-100 + 100, -300) = (0, -300).
Final coordinates relative to the school are (0, -300). Since the y-coordinate is -300 (negative y is South) and the x-coordinate is 0, the home lies 300 m to the South of the school.
Answer: South, 300 m