Samarth walks 10 kms towards east, then takes a right turn and walks 8 kms and again takes a left and walks 6 kms. In which direction is Samarth with respect to his starting position?
South east
Understanding Samarth's Direction from Starting Position
This question asks us to determine Samarth's final direction relative to his starting point after a series of movements involving different directions and turns. Let's break down his path step-by-step to find the solution.
Tracing Samarth's Path and Directions
We can visualize Samarth's journey by considering his starting point as the origin and tracking his displacement in the East-West and North-South directions.
- Starting Point: Let's assume Samarth starts at point O.
- First Movement: He walks 10 kms towards the East. From the starting point O, he moves 10 km East to reach a point, say A. His position is now 10 km East of O.
- Second Movement: He takes a right turn and walks 8 kms. When facing East, a right turn means turning towards the South. So, from point A, he walks 8 km South to reach a point, say B. His position is now 10 km East and 8 km South of O.
- Third Movement: He again takes a left turn and walks 6 kms. When facing South, a left turn means turning towards the East. So, from point B, he walks 6 km East to reach a point, say C. His final position is C.
Determining Final Position Relative to Starting Point
To find Samarth's final direction from his starting position (O), we need to calculate his total displacement in the East-West and North-South directions from O to C.
- Total movement in the East direction: Samarth first moved 10 km East and then another 6 km East. Total Eastward displacement = 10 km + 6 km = 16 km East.
- Total movement in the South direction: Samarth moved 8 km South. Total Southward displacement = 8 km South.
Samarth's final position C is 16 km East and 8 km South of his starting point O.
Finding the Final Direction
If a point is located East and South of a reference point, the direction of that point with respect to the reference point is South-East.
Since Samarth's final position is 16 km East and 8 km South of his starting point, his direction from the starting position is South-East.
| Step | Direction | Distance (kms) | Turn |
|---|---|---|---|
| 1 | East | 10 | None |
| 2 | South | 8 | Right (from East) |
| 3 | East | 6 | Left (from South) |
Therefore, Samarth is in the South-East direction with respect to his starting position.
Revision Table: Key Direction Concepts
| Facing Direction | Right Turn | Left Turn |
|---|---|---|
| North | East | West |
| East | South | North |
| South | West | East |
| West | North | South |
Additional Information: Direction and Displacement
In direction and distance problems, it's important to distinguish between distance traveled and displacement. The total distance traveled is the sum of the lengths of all segments of the path. Displacement is the shortest straight-line distance and direction from the starting point to the ending point.
To find the displacement distance, you would use the Pythagorean theorem if the final position creates a right-angled triangle with the start point (which it does in this case, with legs 16 km East and 8 km South). The displacement distance would be $\sqrt{16^2 + 8^2}$. However, the question only asks for the direction, not the displacement distance.
Visualizing the path on a simple North-South-East-West coordinate system is very helpful for solving these types of direction problems. Start at the origin (0,0). East is along the positive x-axis, North is along the positive y-axis, West is along the negative x-axis, and South is along the negative y-axis.
- 10 km East: Moves to (10, 0).
- Right turn (South), 8 km: Moves from (10, 0) 8 km South to (10, -8).
- Left turn (East), 6 km: Moves from (10, -8) 6 km East to (10+6, -8) = (16, -8).
The final position is (16, -8) relative to the start (0,0). A point with a positive x-coordinate and a negative y-coordinate is in the South-East quadrant.
Similar Questions
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Important Questions from Direction and Distance
Sita took an auto from her home in Andheri (A) to go to her college in Fatehpuri (F). Rather than continuing straight on the direct road to the college that had no turns, the auto driver took a diversion after 10 km and tumed right at Bandra (B) crossing, then at Colaba T- point (C) after 8 km turned left, again after covering 12 km turned left at Dalhousi Building (D) and soon after 8 km turned right at Elphinston point (E) and after covering 4 km reached Fatehpuri (F). Had the auto driver taken the direct route how much less distance would Sita have actually travelled between the starting point and the destination?
Radha walks a distance of 9 m towards the South-East. Then she walks 15 m towards the West. From here, she walks 9 m towards the North-West. Finally she walks 6 m towards the East and stands at the point. How far is she standing from the starting point?
According to the time by Nihaal's watch its half past one and the hour hand is pointing towards the north-east. Assuming that there is no change in Nihaal's position, in which direction would the minute hand point after 30 minutes?
According to the time by Rohan's watch, it is half past 6 and the watch's hands are pointing to the south. In which of the given directions will the minute-hand point AFTER exactly 24 hours?
According to the time by Rick's watch its quarter past eight. If the minute hand points towards the east, towards which direction would the hour hand point?
