Rahul walked 30 m towards North and then he took a left turn and walked 10 m…
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Rahul walked 30 m towards North and then he took a left turn and walked 10 m then he again took a left turn and walked 6 m. Find the shortest distance and in which direction is he from the starting point?
- A.
25 m Northeast
- B.
26 m Northwest
- C.
25 m Northwest
- D.
26 m Northeast
Attempted by 16 students.
Show answer & explanation
Correct answer: B
Key idea: Use coordinates and the Pythagorean theorem to find the displacement.
Start at the origin (0, 0). Walking 30 m north gives position (0, 30).
Turning left (to the west) and walking 10 m moves to (-10, 30).
Turning left again (to the south) and walking 6 m moves to (-10, 24).
The displacement from the starting point is the vector from (0, 0) to (-10, 24).
Shortest distance = sqrt((−10)^2 + 24^2) = sqrt(100 + 576) = sqrt(676) = 26 m.
Direction: x is negative (west) and y is positive (north), so the final position is to the northwest of the starting point.
Answer: 26 m Northwest