Understanding Sanjeev's Journey
This problem involves tracking the movement of Sanjeev in different directions and calculating his final position relative to his starting point. We need to find both the net distance and the direction.
Step-by-Step Movement Analysis
Let's break down Sanjeev's journey step by step:
- Initial Move: Sanjeev travels 3 km towards the East.
- Second Move: He turns South and travels 3 km.
- Third Move: He turns East again and travels 6 km.
- Final Move: He turns North and travels 15 km.
Calculating Net East-West Displacement
We first sum up all the movements along the East-West axis. Movement towards the East is considered positive, and West is negative.
- Movement East: 3 km + 6 km = 9 km
- Movement West: 0 km
- Net Horizontal Displacement: 9 km towards the East.
Calculating Net North-South Displacement
Next, we sum up all the movements along the North-South axis. Movement towards the North is considered positive, and South is negative.
- Movement North: 15 km
- Movement South: 3 km
- Net Vertical Displacement: 15 km (North) - 3 km (South) = 12 km towards the North.
Determining Final Distance from Starting Point
Sanjeev's final position is 9 km East and 12 km North of his starting point. These two displacements form the legs of a right-angled triangle. The distance from the starting point is the hypotenuse of this triangle. We can use the Pythagorean theorem to calculate this distance:
Let $d$ be the net distance from the starting point.
According to the Pythagorean theorem: $d^2 = (\text{Net Horizontal Displacement})^2 + (\text{Net Vertical Displacement})^2$
Substituting the values:
$$ d^2 = (9 \text{ km})^2 + (12 \text{ km})^2 $$ $$ d^2 = 81 \text{ km}^2 + 144 \text{ km}^2 $$ $$ d^2 = 225 \text{ km}^2 $$ $$ d = \sqrt{225 \text{ km}^2} $$ $$ d = 15 \text{ km} $$Determining Final Direction from Starting Point
Since the net horizontal displacement is towards the East (9 km) and the net vertical displacement is towards the North (12 km), Sanjeev's final position relative to his starting point is in the North-East direction.
Conclusion
Combining the distance and direction, Sanjeev is 15 km away from his starting point in the North-East direction.
Important Questions from Direction and Distance
Mukesh was facing the south. He walked 5 km straight and from there he turned at a 90° angle to his right and walked 5 km. Then he turned at a 45° angle to his left and walked 3 km. Where will he be from his actual position?
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?
