A red and a blue car leave Bellevue at the same time. The red car drives south and the blue car drives west. The red car is going 65 kilometers per hour and the blue car is going 75 kilometers per hour. The day is sunny. After 4 hours, a) how far apart are the cars? kilometers b) how fast is the distance between the cars changing? km/hr (Enter each answer as decimal rounded to 2 places.) Show all work, including a drawing labeled with the variables you are using.
A red and a blue car leave Bellevue at the same time. The red car drives south and the blue car drives west. The red car is going 65 kilometers per hour and the blue car is going 75 kilometers per hour. The day is sunny. After 4 hours, a) how far apart are the cars? kilometers b) how fast is the distance between the cars changing? km/hr (Enter each answer as decimal rounded to 2 places.) Show all work, including a drawing labeled with the variables you are using.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:**Problem: Motion and Distance Calculation**
**Scenario:**
A red and a blue car leave Bellevue at the same time. The red car drives south and the blue car drives west. The red car is traveling at a speed of 65 kilometers per hour, while the blue car is traveling at 75 kilometers per hour. The day is sunny.
**Questions:**
**After 4 hours:**
a) How far apart are the cars?
b) How fast is the distance between the cars changing?
(Enter each answer as a decimal rounded to 2 places.)
**Instructions:** Show all work, including a drawing labeled with the variables you are using.
**Explanation:**
1. **Distance Traveled:**
- **Red Car:** Distance = Speed × Time = 65 km/h × 4 h = 260 km
- **Blue Car:** Distance = Speed × Time = 75 km/h × 4 h = 300 km
2. **Calculating Distance Apart:**
- Use the Pythagorean theorem, as the cars move perpendicularly.
- Distance apart = √(260² + 300²) km.
3. **Rate of Change of Distance:**
- Differentiate the distance formula with respect to time to find the rate of change.
- Use the formula: dD/dt = (x*x' + y*y') / D, where x and y are distances, x' and y' are speeds, and D is the distance apart.
This is a classic physics problem involving relative motion and geometry.
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