Mehar drives 19 km East from his home. He then takes a left turn and drives 11 km. He again takes a left turn and drives 19 km. How far is he from starting point in a straight line?
11 km
Understanding the Direction and Distance Problem
This question asks us to determine the straight-line distance of a person, Mehar, from his starting point after completing a series of movements involving different directions and turns. These types of problems require careful tracking of movement relative to the starting position.
Step-by-Step Movement Analysis
Let's break down Mehar's journey into individual steps:
- Mehar starts at his home (let's call this the Starting Point).
- He drives 19 km East from his home.
- He takes a left turn. When facing East, a left turn means turning towards North. He then drives 11 km in the North direction.
- He again takes a left turn. When facing North, a left turn means turning towards West. He then drives 19 km in the West direction.
Calculating the Final Distance from the Starting Point
To find the straight-line distance from the starting point, we need to consider the net displacement in the East-West and North-South directions.
- East-West Movement: Mehar first drives 19 km East and then drives 19 km West. These two movements are in opposite directions and cover the same distance. Therefore, his net displacement in the East-West direction is \(19 \text{ km (East)} - 19 \text{ km (West)} = 0 \text{ km}\). This means his final position is directly North or South of his starting point.
- North-South Movement: Mehar drives 11 km in the North direction. There is no movement in the South direction. Therefore, his net displacement in the North-South direction is 11 km North.
Since the net East-West displacement is 0 km and the net North-South displacement is 11 km North, Mehar's final position is 11 km directly North of his starting point.
The straight-line distance from the starting point is simply the magnitude of this net displacement.
Distance = Net North-South displacement = 11 km.
Final Answer Determination
Based on the analysis of Mehar's movements, his final position is 11 km away from his starting point in a straight line.
Revision Table: Key Concepts in Direction and Distance
| Direction | Left Turn From | Right Turn From |
|---|---|---|
| East | North | South |
| West | South | North |
| North | West | East |
| South | East | West |
Additional Information: Solving Directional Problems
Solving direction and distance problems often involves visualizing the path or drawing a diagram. For movements along cardinal directions (North, South, East, West), you can consider movements along perpendicular axes (like an x-y grid). East is typically considered positive on the x-axis, West as negative on the x-axis, North as positive on the y-axis, and South as negative on the y-axis.
- Movements in opposite directions cancel each other out if the distance is the same.
- For more complex paths that form a right-angled triangle relative to the start and end points, the Pythagorean theorem (\(a^2 + b^2 = c^2\)) can be used to find the straight-line distance.
- Pay close attention to whether the question asks for the total distance traveled or the straight-line distance from the starting point. This question specifically asks for the "distance from starting point in a straight line".
Similar Questions
After leaving school, Hemant and Anurag walk towards the north for 1 km to reach a bus stop. From the bus stop, Hemant turns left and walks for 500 m. Then he turns towards his left and walks for 2 km to reach his home. From the bus stop, Anurag turns right and walks for 250 m. Then he turns right and walks for 1 km to reach his home. In which direction is Anurag's home from Hemant's home?
Tamanna is walking towards the north from her house. After 500 metres she turns left and walks for 500 metres. Then she turns left and walks 250 metres to reach her friend’s house. In Which direction is her house from her friend’s house?
Starting from a point A, an animal walked 15 m towards East. It took a left turn and walked 25 m. Then, it took a right turn and walked 10 m. Again it took a left turn and walked 15 m. Finally, it took a left turn and walked 25 m. How far and in which directions is the animal now from the starting point A?
- Sumit is facing north-east, and then he turns 90° clockwise. After that, he turns 135° anticlockwise. Finally, he turns 90° clockwise. In which direction is he facing now?
The length and breadth of a hall are 16 m and 13 m, respectively. A dog runs along all four walls once to catch the bone. How much total distance does the dog cover?
Gurman drove 28 km towards the West, took a left turn and drove 22 km. She then took a right turn and drove 18 km. She again took a right turn and drove 22 km. How far is she from starting point in a straight line?
Indira starts from point A, which is 7 km towards East of point B. From point A, she drives 4 km towards East. From here, she takes a left turn and drives 9 km. She then takes a left turn, drives 9 km and stops at point C. If from point C, Indira drives 9 km towards South, how far will she be from point B?
Manjot cycles X km towards North and then turns left and cycles Y km to reach her shop. The shortest distance between the starting point and her shop is 5 km. What can be the value of X and Y in km?
One evening when Rosy was going to the market, she saw the Sun to her right. She walked for 100 metres and turned left and walked 50 metres to reach a crossroad. From there she walked towards the south for 40 Metres, and finally she turned left and walked 60 metres to reach the market. In which direction is the market from her house?
Maheep starts walking from his office and walks 120 m towards south. Then he turns left and walks a certain distance A m. Then turns right and walks 80 m. Then he turns left and walks another certain distance B m. He there by reaches his home. If the shortest distance between his office and home is 290 m, then what is the sum of the distances A and B that Maheep covered/walked?
Important Questions from Direction and Distance Turns
After leaving school, Hemant and Anurag walk towards the north for 1 km to reach a bus stop. From the bus stop, Hemant turns left and walks for 500 m. Then he turns towards his left and walks for 2 km to reach his home. From the bus stop, Anurag turns right and walks for 250 m. Then he turns right and walks for 1 km to reach his home. In which direction is Anurag's home from Hemant's home?
A bank employee drives 10 km towards South from her house and turns to her left and drives another 20 km. She again turns left and drives 40 km, then she turns to her right and drives for another 5 km. She again turns to her right and drives another 30 km to reach her bank where she works. What is the shortest distance between her bank and her house ?
A woman runs 12 km towards her North, then 6 km towards her South and then 8 km towards her East. In which direction is she from her starting point ?
Two friends Xand Ystart running and they run together for 50 m in the same direction and reach a point. Xturns right and runs 60 m, while Yturns left and runs 40 m. Then Xturns left and runs 50 m and stops, while Yturns right and runs 50 m and then stops. How far are the two friends from each other now?
Rohan walks 10 km towards north from a point A. Then he turns right and walks 6 km. Then, he again turns right and walks 10 km. In which direction is he now from the starting point?
