Diya runs 10 metres towards north. Then she turns right and runs 20 metres. Again she turns right and runs 35 metres. Then she turns left and runs 10 metres. Finally she turns left and runs 10 m. In which direction and how many metres is she from the starting position?
Question
Diya runs 10 metres towards north. Then she turns right and runs 20 metres. Again she turns right and runs 35 metres. Then she turns left and runs 10 metres. Finally she turns left and runs 10 m. In which direction and how many metres is she from the starting position?
Solution
Diya's movements can be tracked as follows:
- She starts by running 10 metres north.
- She then turns right (which would be east if facing north) and runs 20 metres.
- She turns right again (now facing south) and runs 35 metres. At this point, she is 25 metres south of her starting position (35 metres south minus the initial 10 metres north).
- She then turns left (now facing east) and runs 10 metres.
- Finally, she turns left again (now facing north) and runs 10 metres. This brings her back to the same latitude as her starting position (10 metres north cancels out the 10 metres south from step 4).
In terms of longitude, she is 30 metres east of her starting position (20 metres east from step 2 plus 10 metres east from step 4).
So, Diya is 30 metres east of her starting position.
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