A person moves towards north with uniform speed of 15 m/s and cover 16 m. After this he moves towards east and covers 6 m and finallt covers 8 m distance with same speed in south. Find out
(i) Distance travelled by person
(ii) Displacement of person
(iii) Average velocity of person

Answer

To solve the problem step by step, let's break it down into the required parts:

### Step 1: Calculate the Total Distance Travelled
The total distance travelled by the person is the sum of all the distances covered in each direction.

- Distance travelled north = 16 m
- Distance travelled east = 6 m
- Distance travelled south = 8 m

**Total Distance = Distance North + Distance East + Distance South**
\[ \text{Total Distance} = 16 \, \text{m} + 6 \, \text{m} + 8 \, \text{m} = 30 \, \text{m} \]

### Step 2: Calculate the Displacement
Displacement is the shortest distance from the initial position to the final position. We can visualize the movements as a right triangle:

1. The person moves north (16 m).
2. Then east (6 m).
3. Finally south (8 m).

To find the final position, we can calculate the net north-south movement:
- Net north-south movement = Distance North - Distance South
\[ \text{Net North-South} = 16 \, \text{m} - 8 \, \text{m} = 8 \, \text{m} \text{ (North)} \]

Now, we have:
- North-South component = 8 m (North)
- East-West component = 6 m (East)

Using the Pythagorean theorem to find the displacement:
\[ \text{Displacement} = \sqrt{(\text{North-South})^2 + (\text{East-West})^2} \]
\[ \text{Displacement} = \sqrt{(8 \, \text{m})^2 + (6 \, \text{m})^2} = \sqrt{64 + 36} = \sqrt{100} = 10 \, \text{m} \]

### Step 3: Calculate the Average Velocity
Average velocity is defined as the total displacement divided by the total time taken.

**Total Time Calculation:**
1. Time taken to travel north:
\[ \text{Time North} = \frac{\text{Distance}}{\text{Speed}} = \frac{16 \, \text{m}}{15 \, \text{m/s}} = \frac{16}{15} \, \text{s} \]
2. Time taken to travel east:
\[ \text{Time East} = \frac{6 \, \text{m}}{15 \, \text{m/s}} = \frac{6}{15} \, \text{s} = \frac{2}{5} \, \text{s} \]
3. Time taken to travel south:
\[ \text{Time South} = \frac{8 \, \text{m}}{15 \, \text{m/s}} = \frac{8}{15} \, \text{s} \]

**Total Time = Time North + Time East + Time South**
\[ \text{Total Time} = \frac{16}{15} + \frac{2}{5} + \frac{8}{15} \]
To add these, convert \(\frac{2}{5}\) to a fraction with a denominator of 15:
\[ \frac{2}{5} = \frac{6}{15} \]
Now, add:
\[ \text{Total Time} = \frac{16}{15} + \frac{6}{15} + \frac{8}{15} = \frac{30}{15} = 2 \, \text{s} \]

**Average Velocity Calculation:**
\[ \text{Average Velocity} = \frac{\text{Total Displacement}}{\text{Total Time}} = \frac{10 \, \text{m}}{2 \, \text{s}} = 5 \, \text{m/s} \]

### Final Answers:
(i) Total Distance travelled = 30 m
(ii) Displacement = 10 m
(iii) Average Velocity = 5 m/s

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