Rahul walks 30 metres towards south. Then turns to his right and starts walking straight till he completes another 30 metres. Then again turning to his left he walks for 20 metres. He then turns to his left and walks for 30 metres. How far is he from his initial position?

(1) 50 metres
(2) 30 metres
(3) 10 metres
(4) 60 metres

Question

High School

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Answer :

DanielJosephParker DanielJosephParker · Answer 1 · 2024-04-29T08:28:23-04:00

To solve this problem, we need to track Rahul's movements and determine his final position relative to his starting point.

Initial Movement: Rahul walks 30 metres towards the south.
First Turn: He then turns to his right, which means he is now facing west, and walks straight for 30 metres.
Second Turn: Again, he turns to his left. Now, turning left from west-facing direction will make him face towards the south again. He walks for another 20 metres.
Third Turn: Finally, Rahul turns to his left from facing south, which will make him face east, and he walks 30 metres.

Let's visualize his movements on a coordinate plane:

Start at origin (0, 0).
First move (south): From (0, 0) to (0, -30).
Second move (west): From (0, -30) to (-30, -30).
Third move (south): From (-30, -30) to (-30, -50).
Fourth move (east): From (-30, -50) to (0, -50).

Now, we need to calculate the distance between his final position, (0, -50), and his starting position, (0, 0).

The distance formula is: [tex]\sqrt{{(x_2-x_1)^2 + (y_2-y_1)^2}}[/tex].

Substitute the coordinates:

[tex]\sqrt{{(0-0)^2 + ((-50)-0)^2}} = \sqrt{{0 + 2500}} = \sqrt{2500} = 50[/tex] metres.

Therefore, the correct answer is:
(1) 50 metres.