To determine the direction of the hospital with respect to Kajal's home, we need to analyze the path she took step by step:
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Kajal starts at her home and travels 5 km towards the East.
- This means she moves horizontally to the right on a map representation.
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Then, she turns towards the South-East and travels 10 km.
- South-East implies she moves diagonally downwards to the right at a 45-degree angle, combining the movement towards the South and East.
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Next, she again turns towards the North-East and travels 10 km.
- North-East implies she moves diagonally upwards to the right at a 45-degree angle, combining the movement towards the North and East.
Now, let's analyze the resultant displacement:
- From the initial position to the point after traveling 5 km East, her coordinates can be considered as (5, 0).
- Moving 10 km to the South-East means adding components in both the southern and eastern directions. This results in approximately (5 + 10cos45°, 0 - 10sin45°), which simplifies to (5 + 7.07, -7.07).
- Moving 10 km North-East again means adding components in the northern and eastern directions. This results in approximately (5 + 7.07 + 10cos45°, -7.07 + 10sin45°), which simplifies to (5 + 14.14, 0).
As a result of these movements, Kajal’s final coordinates are approximately (19.14, 0) with respect to her home. Therefore, she is located directly to the East of her starting point.
Conclusion: The hospital is in the East direction from Kajal's home.
Important Questions from Direction and Distance (Notes)
- If a map is placed in such a manner that east becomes southeast, then what will northeast become?
- The door of Aman's house faces east. From the back side of his house, Aman walks straight 30m. Again he walks 20m after turning to his left, then he turns to his right and walks 30m. Finally he turn towards north and walks 20m and stops. So, what is the distance between the starting and the end point?
- A woman leaves her home. She walks 40 m in North-West direction and then 90 m in South-East direction. Then, she moves 30 m in North direction. How far is she now from her initial position ?
- N sits to the North of L and West of M. L sits to the East of O. If everyone is facing North, which direction of O, is N?
I starts from Point A and drives 5 km towards the north. He then takes a right turn, drives 2 km, turns right and drives 9 km. He then takes a right turn and drives 7 km. He takes a final right turn, drives 4 km and stops at Point P. How far (shortest distance) and towards which direction should he drive in order to reach Point A again? (All turns are $90^\circ$ turns only unless specified.)
