Calculating Anna's Final Position
The problem asks for the distance and direction Anna is from her starting point after a series of movements. This is a displacement problem.
Analyzing Anna's Movements
- Initial Movement: Anna walks 15 meters south.
- Second Movement: She turns right. Since she was walking south, turning right means she now walks west. She walks 20 meters west.
These movements can be visualized as two perpendicular legs of a right-angled triangle, where the starting point is one vertex, the point after walking south is another, and the final point is the third vertex.
Finding the Distance from the Starting Point
The distance from the starting point is the hypotenuse of the right-angled triangle formed by her path. We can use the Pythagorean theorem:
Distance$^2$ = (Southward distance)$^2$ + (Westward distance)$^2$
Let $d$ be the distance from the starting point.
$ d^2 = (15 \text{ m})^2 + (20 \text{ m})^2 $
$ d^2 = 225 \text{ m}^2 + 400 \text{ m}^2 $
$ d^2 = 625 \text{ m}^2 $
$ d = \sqrt{625 \text{ m}^2} $
$ d = 25 \text{ m} $
Determining the Direction
Anna moved 15 meters south and 20 meters west. Therefore, her final position relative to the starting point is in the south-west direction.
Final Displacement
Combining the distance and direction, Anna is 25 meters south-west from her starting point.
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?
