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A lady runs 12 km towards North then 6 km towards South and then 8 km East. How far is she from her starting point and in which direction
- a)5 km North-East
- b)5 km East
- c)10 km North-East
- d)10 km West
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A lady runs 12 km towards North then 6 km towards South and then 8 km ...
Solution:
The lady runs 12 km towards North, 6 km towards South and 8 km towards East. Let us represent these directions on a graph as shown below:
```
N
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12
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| x
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|6 | 8
| E -------------
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S W
```
From the above graph, we can see that the lady moves 6 km towards the South from her starting point. Therefore, her current position is 12 km North and 6 km South of the starting point, which results in a net displacement of 6 km towards the North.
Further, she moves 8 km towards the East from her current position. Therefore, her current position is 6 km towards the North and 8 km towards the East of the starting point.
Now, we can apply the Pythagoras theorem to calculate the distance between her current position and the starting point.
Distance = √(6² + 8²) km = √100 km = 10 km
Therefore, the lady is 10 km away from her starting point.
To determine the direction, we can use trigonometry.
tan θ = (Opposite side)/(Adjacent side) = 6/8
θ = tan⁻¹(6/8) = 36.87°
Therefore, the direction is 36.87° North-East.
But as per the options given, the nearest direction is 10 km North-East. Therefore, the correct answer is option (c) 10 km North-East.
The lady runs 12 km towards North, 6 km towards South and 8 km towards East. Let us represent these directions on a graph as shown below:
```
N
|
12
|
|
|
| x
| |
| |
| |
| |
| |
| |
| |
|6 | 8
| E -------------
| |
| |
| |
| |
| |
| |
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| |
| |
S W
```
From the above graph, we can see that the lady moves 6 km towards the South from her starting point. Therefore, her current position is 12 km North and 6 km South of the starting point, which results in a net displacement of 6 km towards the North.
Further, she moves 8 km towards the East from her current position. Therefore, her current position is 6 km towards the North and 8 km towards the East of the starting point.
Now, we can apply the Pythagoras theorem to calculate the distance between her current position and the starting point.
Distance = √(6² + 8²) km = √100 km = 10 km
Therefore, the lady is 10 km away from her starting point.
To determine the direction, we can use trigonometry.
tan θ = (Opposite side)/(Adjacent side) = 6/8
θ = tan⁻¹(6/8) = 36.87°
Therefore, the direction is 36.87° North-East.
But as per the options given, the nearest direction is 10 km North-East. Therefore, the correct answer is option (c) 10 km North-East.
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A lady runs 12 km towards North then 6 km towards South and then 8 km East. How far is she from her starting point and in which directiona)5 km North-Eastb)5 km Eastc)10 km North-Eastd)10 km WestCorrect answer is option 'C'. Can you explain this answer?
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