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A man walks 7 km in the North direction. He then walks 4 km Eastward, and then 4 km Southward. How far and in which direction is he now from his original position?
Explanation
To determine the man's final position relative to his starting point, we can track his movements on a coordinate system (starting at 0,0):
- Step 1: He walks 7 km North, reaching point (0, 7).
- Step 2: He walks 4 km East, reaching point (4, 7).
- Step 3: He walks 4 km South. His new vertical position is 7 - 4 = 3 km. His final coordinates are (4, 3).
To find the displacement (distance) from the origin (0,0) to (4,3), we use the Pythagoras theorem:
Distance = √(42 + 32) = √(16 + 9) = √25 = 5 km
Since his final position (4, 3) is 4 km to the East and 3 km to the North of the starting point, he is in the North-East direction. Therefore, he is 5 km away in the North-East direction.
SIMILAR QUESTIONS
‘R walks 1 km. to east and then he turns to south and walks 5 km. Again he turns to east and walks 2 km. After this he turns to north and walks 9 km. How far is he from his starting point ?
A man starts walking in the north-easterly direction from a particular point. After walking a distance of 500 metres, he turns southward and walks a distance of 400 metres. At the end of this walk he is situated
Facing the east R walks straight 4 km, turns left and walks 3 km and again turns left and walks 4 km. How far is R now from the starting point?
R walks a long distance every Sunday. He walks 2 km towards the north from his house and then turns right; he walks another 2 km and again turns right; next he walks 5 km and turns left; he further walks 2 km and stops. He rests for some time and returns home following a straight route without any turning point. What is the distance R walks after he has rested ?