A girl of height 100 cm is walking away from the base of a lamp post at a speed of 1.9 m/s . If the lamp is 5 m above the ground , find the length of her shadow after 4 seconds (in metres )

Answer

To solve the problem step by step, we will follow the reasoning outlined in the video transcript.

### Step-by-Step Solution:

1. **Identify Given Information:**
- Height of the girl (h_g) = 100 cm = 1 m (since 100 cm = 1 m)
- Height of the lamp post (h_l) = 5 m
- Speed of the girl (v) = 1.9 m/s
- Time (t) = 4 seconds

2. **Calculate the Distance the Girl Walks:**
- The distance (d) the girl walks in 4 seconds can be calculated using the formula:
\[ d = v \times t \]
- Substituting the values:
\[ d = 1.9 \, \text{m/s} \times 4 \, \text{s} = 7.6 \, \text{m} \]

3. **Set Up the Problem:**
- Let \( x \) be the length of the shadow.
- The total distance from the lamp post to the tip of the shadow is:
\[ \text{Distance from lamp post to girl} + \text{Length of shadow} = 7.6 + x \]

4. **Use Similar Triangles:**
- We can use the concept of similar triangles. The triangles formed by the lamp post and the girl with their respective shadows are similar.
- The ratio of the heights to the lengths of the bases of the triangles gives us:
\[ \frac{h_l}{7.6 + x} = \frac{h_g}{x} \]
- Substituting the known heights:
\[ \frac{5}{7.6 + x} = \frac{1}{x} \]

5. **Cross Multiply to Solve for x:**
- Cross multiplying gives:
\[ 5x = 7.6 + x \]

6. **Rearranging the Equation:**
- Rearranging the equation:
\[ 5x - x = 7.6 \]
\[ 4x = 7.6 \]

7. **Solve for x:**
- Dividing both sides by 4:
\[ x = \frac{7.6}{4} = 1.9 \, \text{m} \]

8. **Conclusion:**
- Therefore, the length of the shadow after 4 seconds is:
\[ \text{Length of shadow} = 1.9 \, \text{m} \]

### Final Answer:
The length of her shadow after 4 seconds is **1.9 meters**.