Kundan walks 11 km towards North. From there he walks 7 Km towards South. Then, he walks 3 Km towards east. How far and in which direction is he with reference to his starting point?a)10 km, eastb)5 km, northc)15 km, south - eastd)5 km, north -eastCorrect answer is option 'D'. Can you explain this answer?

Question

Answer

Given Information:
Kundan walks 11 km towards North.
From there he walks 7 km towards South.
Then, he walks 3 km towards East.

To Find:
The distance and direction of Kundan from his starting point.

Solution:
To find the distance and direction of Kundan from his starting point, we can use the concept of vectors. We can represent the distance and direction using a vector diagram.

Step 1: Represent the distance and direction of Kundan's movements:
- Kundan walks 11 km towards North.
This can be represented as a vector pointing upwards with a magnitude of 11 km.

- From there, he walks 7 km towards South.
This can be represented as a vector pointing downwards with a magnitude of 7 km.

- Then, he walks 3 km towards East.
This can be represented as a vector pointing towards the right with a magnitude of 3 km.

Step 2: Combine the vectors:
To find the resultant vector, we can combine the individual vectors by adding them up.

- The vector pointing upwards with a magnitude of 11 km cancels out with the vector pointing downwards with a magnitude of 7 km. This is because they have the same magnitude but opposite directions.

- The resultant vector is the vector pointing towards the right with a magnitude of 3 km.

Step 3: Find the magnitude and direction of the resultant vector:
The magnitude of the resultant vector is given by the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (longest side) is equal to the sum of the squares of the other two sides.

In this case, the magnitude of the resultant vector is given by:
magnitude = sqrt((11 km)^2 + (7 km)^2 + (3 km)^2)
= sqrt(121 km^2 + 49 km^2 + 9 km^2)
= sqrt(179 km^2)
= 13.38 km (approx.)

The direction of the resultant vector can be found using trigonometry. We can use the tangent function to find the angle between the resultant vector and the x-axis.

angle = tan^(-1)((sum of y-components) / (sum of x-components))
= tan^(-1)((11 km - 7 km) / 3 km)
= tan^(-1)(4 km / 3 km)
= tan^(-1)(4/3)
= 53.13 degrees (approx.)

Step 4: Final Answer:
Therefore, Kundan is approximately 13.38 km away from his starting point in the north-east direction.

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