Kokila turned 45 degrees right, then 90° left and then 45° right and is now moving towards east. Which direction she was heading in before?
East
Understanding Directional Movements and Net Change
The question asks about Kokila's initial direction before a series of turns, given her final direction. We are told she made three turns and ended up facing East. To find the starting direction, we need to analyze the total effect of her turns.
Step-by-Step Analysis of Turns
Let's list the turns Kokila made:
- Turn 1: 45 degrees right
- Turn 2: 90 degrees left
- Turn 3: 45 degrees right
Calculating the Net Turn
To find the overall change in direction, we can sum up the right turns and the left turns separately, and then find the difference. A right turn is opposite in effect to a left turn.
- Total Right Turn = 45° + 45° = 90° Right
- Total Left Turn = 90° Left
Now, we find the net change:
\text{Net Turn} = \text{Total Right Turn} - \text{Total Left Turn}
\text{Net Turn} = 90° \text{ Right} - 90° \text{ Left}
\text{Net Turn} = 0°
A net turn of 0 degrees means that after all the movements, Kokila is facing in the exact same direction she was facing before starting the turns.
Determining the Initial Direction
We know that after the turns, Kokila is moving towards the East direction. Since the total change in direction was 0 degrees, her initial direction must have been the same as her final direction.
- Final Direction: East
- Net Change: 0°
- Initial Direction = Final Direction
Therefore, Kokila was heading in the East direction before she started making the turns.
| Turn | Direction | Angle |
|---|---|---|
| 1 | Right | 45° |
| 2 | Left | 90° |
| 3 | Right | 45° |
| Total Right Turn | Total Left Turn | Net Turn |
|---|---|---|
| 90° | 90° | 0° |
Since the net turn is zero, the initial direction is the same as the final direction, which is East.
Important Questions from Direction and Distance
- Vijendra walks a certain distance, say X metres, from his home towards the west. Then he turns left and walks 23 metres. After that, he turns left and walks 36 metres. Then he turns left again to walk 23 metres. He finally turns left and walks 18 metres to reach his home. Find the value of X.
Gaurav exits from the backdoor of his north-facing house and walks 25 m straight, then he takes a left turn and walks 36 m, then he turns left and walks 47 m. He turns left again and walks 36 m. How far and in which direction is he from his house now?
Reeta is standing facing south-east. First, she turns 135° clockwise. After that, she turns 90 ° anticlockwise. Then she turns 45 ° clockwise, followed by a 135 ° anticlockwise turn. In which direction is she facing now?
Sahasra started running from her house towards the north. After 40 meters she turned left and ran for 75 meters. She then turned right and ran for 30 meters, and again turned right to run 75 meters. In which direction was she running finally?
At the time of sunset, Lopa and Kritika are sitting facing each other. If the shadow of Lopa falls to the right of Kritika, in which direction is Kritika facing?
