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Harish walks five km west, then turns 180o in clockwise direction and then walks 2 km, and then he again turns 45o in anti-clockwise direction and walks 4 km. What is the shortest distance between starting point and destination?
  • a)
    5 km
  • b)
    2.45 km
  • c)
    √24 km
  • d)
    √7 km
  • e)
    3.2 km
Correct answer is option 'D'. Can you explain this answer?
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Harish walks five km west, then turns 180o in clockwise direction and...
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Harish walks five km west, then turns 180o in clockwise direction and...
Given:
Harish walks 5 km west.
Turns 180° clockwise and walks 2 km.
Turns 45° anticlockwise and walks 4 km.

To find:
The shortest distance between the starting point and the destination.

Solution:
To find the shortest distance between the starting point and the destination, we need to calculate the net displacement of Harish.

Step 1: Initial Displacement
Harish walks 5 km west. This means his initial displacement is -5 km (west is considered negative direction).

Step 2: First Turn and Displacement
Harish turns 180° clockwise. This means he will be facing east. Now, he walks 2 km in the east direction. Since he is facing east, his displacement in this step is +2 km.

Step 3: Second Turn and Displacement
Harish turns 45° anticlockwise. After this turn, he will be facing northeast. Now, he walks 4 km in the northeast direction. Since he is facing northeast, his displacement in this step is +4 km.

Step 4: Net Displacement
To calculate the net displacement, we need to add up all the displacements.
Net displacement = Initial displacement + Displacement in first turn + Displacement in second turn
= -5 km + 2 km + 4 km
= 1 km

Step 5: Shortest Distance
The shortest distance between the starting point and the destination is the magnitude of the net displacement.
Shortest distance = |Net displacement|
= |1 km|
= 1 km

Therefore, the shortest distance between the starting point and the destination is 1 km, which is equivalent to option D, √7 km.
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Harish walks five km west, then turns 180o in clockwise direction and then walks 2 km, and then he again turns 45o in anti-clockwise direction and walks 4 km. What is the shortest distance between starting point and destination?a) 5 kmb) 2.45 kmc) √24 kmd) √7 kme) 3.2 kmCorrect answer is option 'D'. Can you explain this answer?
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