Overtaking and overtaken vehicles are at 70 and 40 kmph respectively. find (i) OSD

1. Break Down the Problem

The problem is about finding the Overhauling Distance (OSD) between two vehicles—one overtaking another. We have:

• Speed of overtaking vehicle (V1) = 70 km/h
• Speed of overtaken vehicle (V2) = 40 km/h

2. Relevant Concepts

To find the Overhauling Distance (OSD), we can use the relative speed concept:

• Relative speed (V_rel) = V1 - V2

The formula for OSD when the two vehicles are moving in the same direction is given as:

$\text{OSD} = \frac{(\text{Length of the overtaking vehicle} + \text{Length of the overtaken vehicle})}{\text{Relative speed}}$

Assuming both vehicles have an average length of 5 meters, we can calculate as follows:

3. Analysis and Detail

1. Calculate Relative Speed (V_rel): $V_{rel} = V1 - V2 = 70 \text{ km/h} - 40 \text{ km/h} = 30 \text{ km/h}$

2. Convert Relative Speed to m/s: Since 1 km/h = $\frac{5}{18}$ m/s, $V_{rel} = 30 \times \frac{5}{18} \approx 8.33 \text{ m/s}$

3. Determine the total length of vehicles: Assuming both have the length of 5 m, the total length is: $\text{Total Length} = 5 \text{ m} + 5 \text{ m} = 10 \text{ m}$

4. Calculate OSD: $\text{OSD} = \frac{10 \text{ m}}{8.33 \text{ m/s}} \approx 1.20 \text{ seconds}$

4. Verify and Summarize

By checking the calculations step by step, the values remain consistent, confirming that our approach is accurate.

Final Answer

The Overhauling Distance (OSD) is approximately 1.20 seconds.