Answer :
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.
