A cyclist moves in such a way that he takes 72° turn towards left after travelling 200 m in straight line. What is the displacement when he takes just takes fourth turn?

Options

A. Zero
B. 600m
C. 400 m
D. 200 m

Answer

To solve the problem of finding the displacement of a cyclist who takes four 72° turns after traveling 200 m in a straight line, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Movement**:
The cyclist starts from an initial point and moves straight for 200 m. After this, he takes a left turn of 72°.

2. **Identifying the Pattern**:
Since the cyclist takes a turn of 72° after every 200 m, we can visualize this as forming a regular polygon. The total angle for a complete turn is 360°, and the cyclist is turning left by 72° each time.

3. **Calculating the Number of Sides**:
To find out how many sides (n) the polygon has, we use the formula:
\[ n = \frac{360°}{\text{angle of turn}} = \frac{360°}{72°} = 5 \]
This means the cyclist is effectively tracing out a regular pentagon.

4. **Visualizing the Turns**:
After the first straight line of 200 m, the cyclist will make the following movements:
- Move 200 m straight (1st side)
- Turn left 72° and move 200 m (2nd side)
- Turn left 72° and move 200 m (3rd side)
- Turn left 72° and move 200 m (4th side)

5. **Determining the Final Position**:
After completing four turns, the cyclist will have moved in a path that returns him to a position that is directly opposite to his starting point in terms of displacement. The distance traveled in each segment is the same (200 m), and the final position forms a triangle with the starting position.

6. **Calculating the Displacement**:
In a regular pentagon, the distance from the starting point to the ending point (the displacement) can be determined. Since the cyclist has made four turns and returned to a position that is effectively the same distance away from the starting point, the displacement will be equal to the length of one side of the pentagon, which is 200 m.

### Final Answer:
The displacement of the cyclist after taking four turns is **200 m**.