5.5k views
0 votes
Ruhani started walking in east and walked 12 m. Now she turned south and walked 4 m and turned to her left and walked 3 m. Now she turned south and walked 7 m. Now to her left and walked 7 m. Now she turned south and walked 8 m, then to west and walked 5 m. Now to her left walking 3 m and finally turned right and walked 3 m. Find the distance from where she started walking.

A) 30 m
B) 25 m
C) 20 m
D) 22 m
E) 18 m​

1 Answer

0 votes

Final answer:

Ruhani's total displacement is calculated by adding her movements in the east/west and north/south directions separately, resulting in 14 m east and 22 m south. Using the Pythagorean theorem, her resultant distance from the starting point is approximately 26.08 m, rounded to the nearest whole number as 26 m, with the closest answer option being 25 m.

Step-by-step explanation:

To find the distance from where Ruhani started walking, we need to consider her path as a series of vector displacements and calculate the resultant vector. Let's go through each step of her walk methodically:

• Walked 12 m east.

• Turned south and walked 4 m.

• Turned to her left (east) and walked 3 m.

• Turned south and walked 7 m.

• Turned to her left (east) and walked 7 m.

• Turned south and walked 8 m.

• Turned west and walked 5 m.

• Turned to her left (south) and walked 3 m.

• Finally, turned right (west) and walked 3 m.

To solve this, we need to keep track of the displacements in both the east/west and north/south directions.

Her net displacement in the east/west direction is: 12 m + 3 m + 7 m - 5 m - 3 m = 14 m east.

Her net displacement in the north/south direction is: 4 m + 7 m + 8 m + 3 m = 22 m south.

Now we use the Pythagorean theorem to find the resulting distance from the starting point:

Resulting distance = √(14 m)2 + (22 m)2

This equals: Resulting distance = √(196 + 484) = √680 m²

Resulting distance ≈ 26.08 m. Rounding to the nearest whole number, the distance is approximately 26 m. Since this option is not listed, the closest value in the options given is 25 m. Therefore, the correct option in the final answer is B) 25 m.

User Dr Alchemy
by
7.3k points

No related questions found