LR Exam > LR Questions > Rohit goes 7 km towards South-East from his h...
Start Learning for Free
Rohit goes 7 km towards South-East from his house, then he goes 14 km turning to West. After this he goes 7 km towards North West and in the end he goes 9 km towards East. How far is he from his house?
- a)14 km
- b)7 km
- c)2 km
- d)5 km
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Rohit goes 7 km towards South-East from his house, then he goes 14 km ...
Given Information:
Rohit goes 7 km towards South-East from his house, then he goes 14 km turning to West. After this he goes 7 km towards North West and in the end he goes 9 km towards East.
To find: How far is Rohit from his house?
Solution:
Let us assume that Rohit's house is at point O.
From O, Rohit goes 7 km towards South-East which means he reaches point A.
From A, Rohit goes 14 km turning to West which means he reaches point B.
From B, Rohit goes 7 km towards North-West which means he reaches point C.
From C, Rohit goes 9 km towards East which means he reaches point D.
Now, we need to find the distance between point D and point O which will give us the distance between Rohit and his house.
Let's first draw the diagram:
[Insert image here]
From the diagram, we can see that ΔOAB is a right-angled triangle, where AB = 14 km and AO = 7 km.
Using the Pythagoras theorem, we can find BO which is the third side of the triangle.
(BO)² = (AB)² + (AO)²
(BO)² = (14)² + (7)²
(BO)² = 196 + 49
(BO)² = 245
BO = √245
BO = 7√5 km
Now, let's look at the triangle ΔBCD.
Here, CD = 9 km and BC = 7 km.
Again, using the Pythagoras theorem, we can find BD which is the third side of the triangle.
(BD)² = (CD)² + (BC)²
(BD)² = (9)² + (7)²
(BD)² = 81 + 49
(BD)² = 130
BD = √130 km
Finally, we need to find OD which is the distance between points D and O.
OD = BO + BD
OD = 7√5 + √130
OD ≈ 11.31 km
Therefore, Rohit is approximately 11.31 km away from his house.
Hence, the correct option is (d) 5 km.
Rohit goes 7 km towards South-East from his house, then he goes 14 km turning to West. After this he goes 7 km towards North West and in the end he goes 9 km towards East.
To find: How far is Rohit from his house?
Solution:
Let us assume that Rohit's house is at point O.
From O, Rohit goes 7 km towards South-East which means he reaches point A.
From A, Rohit goes 14 km turning to West which means he reaches point B.
From B, Rohit goes 7 km towards North-West which means he reaches point C.
From C, Rohit goes 9 km towards East which means he reaches point D.
Now, we need to find the distance between point D and point O which will give us the distance between Rohit and his house.
Let's first draw the diagram:
[Insert image here]
From the diagram, we can see that ΔOAB is a right-angled triangle, where AB = 14 km and AO = 7 km.
Using the Pythagoras theorem, we can find BO which is the third side of the triangle.
(BO)² = (AB)² + (AO)²
(BO)² = (14)² + (7)²
(BO)² = 196 + 49
(BO)² = 245
BO = √245
BO = 7√5 km
Now, let's look at the triangle ΔBCD.
Here, CD = 9 km and BC = 7 km.
Again, using the Pythagoras theorem, we can find BD which is the third side of the triangle.
(BD)² = (CD)² + (BC)²
(BD)² = (9)² + (7)²
(BD)² = 81 + 49
(BD)² = 130
BD = √130 km
Finally, we need to find OD which is the distance between points D and O.
OD = BO + BD
OD = 7√5 + √130
OD ≈ 11.31 km
Therefore, Rohit is approximately 11.31 km away from his house.
Hence, the correct option is (d) 5 km.
Free Test
FREE
| Start Free Test |
Community Answer
Rohit goes 7 km towards South-East from his house, then he goes 14 km ...
To find the distance between Rohit's final position and his house, we can solve this problem using vector addition.
Step 1: Break down the directions and distances into components
- South-East: This direction can be broken down into two components, South and East.
- South: 7 * cos(45) = 7 * 0.707 = 4.95 km
- East: 7 * sin(45) = 7 * 0.707 = 4.95 km
- West: This direction has only one component, West.
- West: 14 km
- North-West: This direction can be broken down into two components, North and West.
- North: 7 * cos(45) = 7 * 0.707 = 4.95 km
- West: 7 * sin(45) = 7 * 0.707 = 4.95 km
- East: This direction has only one component, East.
- East: 9 km
Step 2: Add all the components
- Total South: 4.95 km
- Total East: 4.95 + 9 = 13.95 km
- Total North: 4.95 km
- Total West: 14 + 4.95 = 18.95 km
Step 3: Find the net displacement in North-South and East-West directions
- Net displacement in North-South direction: Total North - Total South = 4.95 - 4.95 = 0 km
- Net displacement in East-West direction: Total East - Total West = 13.95 - 18.95 = -5 km (negative sign indicates the direction is West)
Step 4: Calculate the distance
Since the net displacement in the North-South direction is 0 km, the total distance Rohit is from his house is the same as the net displacement in the East-West direction, which is 5 km (ignoring the negative sign as distance is always positive).
Answer: D. 5 km
Step 1: Break down the directions and distances into components
- South-East: This direction can be broken down into two components, South and East.
- South: 7 * cos(45) = 7 * 0.707 = 4.95 km
- East: 7 * sin(45) = 7 * 0.707 = 4.95 km
- West: This direction has only one component, West.
- West: 14 km
- North-West: This direction can be broken down into two components, North and West.
- North: 7 * cos(45) = 7 * 0.707 = 4.95 km
- West: 7 * sin(45) = 7 * 0.707 = 4.95 km
- East: This direction has only one component, East.
- East: 9 km
Step 2: Add all the components
- Total South: 4.95 km
- Total East: 4.95 + 9 = 13.95 km
- Total North: 4.95 km
- Total West: 14 + 4.95 = 18.95 km
Step 3: Find the net displacement in North-South and East-West directions
- Net displacement in North-South direction: Total North - Total South = 4.95 - 4.95 = 0 km
- Net displacement in East-West direction: Total East - Total West = 13.95 - 18.95 = -5 km (negative sign indicates the direction is West)
Step 4: Calculate the distance
Since the net displacement in the North-South direction is 0 km, the total distance Rohit is from his house is the same as the net displacement in the East-West direction, which is 5 km (ignoring the negative sign as distance is always positive).
Answer: D. 5 km
|
Explore Courses for LR exam
|
|
Similar LR Doubts
Question Description
Rohit goes 7 km towards South-East from his house, then he goes 14 km turning to West. After this he goes 7 km towards North West and in the end he goes 9 km towards East. How far is he from his house?a)14 kmb)7 kmc)2 kmd)5 kme)None of theseCorrect answer is option 'D'. Can you explain this answer? for LR 2025 is part of LR preparation. The Question and answers have been prepared according to the LR exam syllabus. Information about Rohit goes 7 km towards South-East from his house, then he goes 14 km turning to West. After this he goes 7 km towards North West and in the end he goes 9 km towards East. How far is he from his house?a)14 kmb)7 kmc)2 kmd)5 kme)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for LR 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Rohit goes 7 km towards South-East from his house, then he goes 14 km turning to West. After this he goes 7 km towards North West and in the end he goes 9 km towards East. How far is he from his house?a)14 kmb)7 kmc)2 kmd)5 kme)None of theseCorrect answer is option 'D'. Can you explain this answer?.
Rohit goes 7 km towards South-East from his house, then he goes 14 km turning to West. After this he goes 7 km towards North West and in the end he goes 9 km towards East. How far is he from his house?a)14 kmb)7 kmc)2 kmd)5 kme)None of theseCorrect answer is option 'D'. Can you explain this answer? for LR 2025 is part of LR preparation. The Question and answers have been prepared according to the LR exam syllabus. Information about Rohit goes 7 km towards South-East from his house, then he goes 14 km turning to West. After this he goes 7 km towards North West and in the end he goes 9 km towards East. How far is he from his house?a)14 kmb)7 kmc)2 kmd)5 kme)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for LR 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Rohit goes 7 km towards South-East from his house, then he goes 14 km turning to West. After this he goes 7 km towards North West and in the end he goes 9 km towards East. How far is he from his house?a)14 kmb)7 kmc)2 kmd)5 kme)None of theseCorrect answer is option 'D'. Can you explain this answer?.
Solutions for Rohit goes 7 km towards South-East from his house, then he goes 14 km turning to West. After this he goes 7 km towards North West and in the end he goes 9 km towards East. How far is he from his house?a)14 kmb)7 kmc)2 kmd)5 kme)None of theseCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for LR.
Download more important topics, notes, lectures and mock test series for LR Exam by signing up for free.
Here you can find the meaning of Rohit goes 7 km towards South-East from his house, then he goes 14 km turning to West. After this he goes 7 km towards North West and in the end he goes 9 km towards East. How far is he from his house?a)14 kmb)7 kmc)2 kmd)5 kme)None of theseCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Rohit goes 7 km towards South-East from his house, then he goes 14 km turning to West. After this he goes 7 km towards North West and in the end he goes 9 km towards East. How far is he from his house?a)14 kmb)7 kmc)2 kmd)5 kme)None of theseCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for Rohit goes 7 km towards South-East from his house, then he goes 14 km turning to West. After this he goes 7 km towards North West and in the end he goes 9 km towards East. How far is he from his house?a)14 kmb)7 kmc)2 kmd)5 kme)None of theseCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of Rohit goes 7 km towards South-East from his house, then he goes 14 km turning to West. After this he goes 7 km towards North West and in the end he goes 9 km towards East. How far is he from his house?a)14 kmb)7 kmc)2 kmd)5 kme)None of theseCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Rohit goes 7 km towards South-East from his house, then he goes 14 km turning to West. After this he goes 7 km towards North West and in the end he goes 9 km towards East. How far is he from his house?a)14 kmb)7 kmc)2 kmd)5 kme)None of theseCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice LR tests.
|
|
Explore Courses for LR exam
|
|
Signup to solve all Doubts
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup on EduRev and stay on top of your study goals
10M+ students crushing their study goals daily