Shalini drives 5 km North, then she turns East and drives 12 km. After this, she turns North and drives 4 km. Again she turns East and drives 5 km. What is the total distance covered by Shalini?
26 km
Calculating Total Distance Covered
This problem asks us to find the total distance Shalini covered during her journey. To do this, we need to add up the distance covered in each separate part of her trip.
Step-by-Step Journey Analysis
Let's break down Shalini's journey into individual segments:
- First movement: Shalini drives 5 km North.
- Second movement: She turns East and drives 12 km.
- Third movement: She turns North and drives 4 km.
- Fourth movement: She turns East and drives 5 km.
The total distance covered is simply the sum of the distances of all these individual movements.
Calculating the Total Distance
We can calculate the total distance by adding the length of each segment:
Total Distance $=$ Distance of Segment 1 + Distance of Segment 2 + Distance of Segment 3 + Distance of Segment 4
Substituting the given values:
Total Distance $=$ $5 \text{ km} + 12 \text{ km} + 4 \text{ km} + 5 \text{ km}$
Now, let's perform the addition:
Total Distance $=$ $(5 + 12 + 4 + 5)$ km
Total Distance $=$ $(17 + 4 + 5)$ km
Total Distance $=$ $(21 + 5)$ km
Total Distance $=$ $26$ km
So, the total distance covered by Shalini is 26 km.
| Movement | Direction | Distance (km) |
|---|---|---|
| 1st | North | 5 |
| 2nd | East | 12 |
| 3rd | North | 4 |
| 4th | East | 5 |
| Total Distance | 26 | |
The calculation confirms that the total distance is 26 km.
Understanding Total Distance vs. Displacement
It is important to distinguish between total distance and displacement.
- Total Distance: This is the total length of the path traveled. It is a scalar quantity, meaning it only has magnitude. We simply add up all the lengths of the segments moved.
- Displacement: This is the straight-line distance between the starting point and the ending point, along with the direction. It is a vector quantity, meaning it has both magnitude and direction. Calculating displacement often involves using geometry or vector addition, especially if the movements are not in a straight line or back and forth along the same line.
In this specific problem, we were asked for the total distance covered, which means we just add up the lengths of all the individual legs of the journey, regardless of direction.
Revision Table: Key Concepts
| Concept | Definition | Type of Quantity | How to Calculate (for this problem) |
|---|---|---|---|
| Total Distance | Total length of the path traveled. | Scalar (Magnitude only) | Sum of distances of each leg of the journey. |
| Displacement | Straight-line distance from start to end point, with direction. | Vector (Magnitude and Direction) | Requires considering direction of each movement (e.g., using Pythagorean theorem or vectors for this journey). |
Additional Information: Calculating Displacement for Shalini's Journey
Although the question asks for total distance, let's briefly consider how displacement would be calculated for Shalini's journey as additional information. This involves vector addition.
Movements:
- North: 5 km, then 4 km. Total North displacement = $5 + 4 = 9$ km North.
- East: 12 km, then 5 km. Total East displacement = $12 + 5 = 17$ km East.
The net movement is 9 km North and 17 km East. These two movements are perpendicular. The magnitude of the displacement (straight-line distance from start to end) can be found using the Pythagorean theorem:
Displacement Magnitude $=$ $\sqrt{(\text{Total North Displacement})^2 + (\text{Total East Displacement})^2}$
Displacement Magnitude $=$ $\sqrt{(9 \text{ km})^2 + (17 \text{ km})^2}$
Displacement Magnitude $=$ $\sqrt{81 \text{ km}^2 + 289 \text{ km}^2}$
Displacement Magnitude $=$ $\sqrt{370} \text{ km}$
So, the displacement magnitude is $\sqrt{370}$ km, which is approximately 19.24 km. This is different from the total distance covered (26 km), highlighting the difference between the two concepts.
Similar Questions
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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?
