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".
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Important Questions from Direction and Distance Turns
Starting from her home, a woman walks 10 km towards the west. She turns left and walks 25 km. Again she turns left and walks 10 km. After that, she again turns left and walks 5 km. How far is she from her house now?
A. 35
B. 20
C. 25
D. 40
Lalit walks 9 km east, turns left and walks another 8 km. He again takes a left and walks another 3 km. How far and in which direction is he now from his starting point?
A boy starts from his home northward in order to go to a hotel. He took right turn and took left to reach the hotel. Which direction is the hotel facing?
Arun went 6 m from his home towards south and turned left to cover 8 m. Again he turned left and covered 6 m. He again turned right and covered 4 m. What was the direct distance from his home and which direction was he facing?
Sri walked 4 km towards east from home to school, and he turned three times right side of 6 km respectively. What is the distance between his home and the school?
