https://file.aiquickdraw.com/mathbot/file/17268585748681k09np04.jpg

Let's break down the problem step by step to solve it.

We are given:
- Car A passes point X at 10:00, traveling to the right at 10 m/s.
- Car B passes point Y at 10:02, traveling to the left at 15 m/s.
- The distance between X and Y is 3 km (3000 meters).

We need to calculate when and where the two cars will meet.

### Step 1: Time delay between car movements
Car A passes point X at 10:00, while Car B passes point Y at 10:02. This means Car A has a 2-minute (or 120-second) head start. During this time, Car A covers a distance:

\[
\text{Distance covered by Car A in 120 seconds} = 10 \, \text{m/s} \times 120 \, \text{seconds} = 1200 \, \text{meters}
\]

At 10:02, when Car B starts moving, Car A is now 1200 meters to the right of point X.

### Step 2: Relative motion and meeting point
Both cars are now moving towards each other. The distance between them is:

\[
3000 \, \text{meters} - 1200 \, \text{meters} = 1800 \, \text{meters}
\]

The relative speed at which they are approaching each other is the sum of their individual speeds:

\[
\text{Relative speed} = 10 \, \text{m/s} + 15 \, \text{m/s} = 25 \, \text{m/s}
\]

### Step 3: Time to meet
The time it will take for the two cars to meet can be calculated using the formula:

\[
\text{Time to meet} = \frac{\text{Distance to be covered}}{\text{Relative speed}} = \frac{1800 \, \text{meters}}{25 \, \text{m/s}} = 72 \, \text{seconds}
\]

Thus, Car A and Car B will meet **72 seconds after 10:02**, which is **10:03:12**.

### Step 4: Position of the meeting point
Now, we calculate the position of the meeting point relative to point X. In these 72 seconds, Car A continues to move to the right, so it covers a distance:

\[
\text{Distance covered by Car A} = 10 \, \text{m/s} \times 72 \, \text{seconds} = 720 \, \text{meters}
\]

Since Car A was already 1200 meters to the right of X, the total distance from X where they meet is:

\[
\text{Position of the meeting point} = 1200 \, \text{meters} + 720 \, \text{meters} = 1920 \, \text{meters}
\]

### Final Answer:
- **Time of meeting**: 10:03:12 (rounded to 10:03).
- **Position of meeting**: 1920 meters to the right of point X.

Let me know if you'd like further details or have any questions.

Here are 5 relative questions:
1. How would the result change if Car B started moving at 10:00 instead of 10:02?
2. What if Car A traveled at a speed of 15 m/s and Car B at 10 m/s?
3. How far would Car A and Car B be after 5 minutes from 10:02 if they continued traveling?
4. How would you solve this problem if Car B had a delayed start of 3 minutes instead of 2?
5. How does the concept of relative velocity help simplify this type of problem?

**Tip**: In problems involving two objects moving towards or away from each other, using relative velocity makes calculations much faster and simpler.

Car A passes point X at 10:00 traveling to the right at 10 m/s. Car B passes point Y at 10:02 traveling to the left at 15 m/s. The distance between X and Y is 3 km. Calculate the time and the position where Car A and Car B will pass each other.

Learn how to calculate the time and position where two cars, traveling at different speeds, will meet on a straight track. This problem involves concepts like relative motion, velocity, and distance. Suitable for high school physics students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation