A road perpendicular to a highway leads to a farmhouse located a = 1.3 km away. An automobile travels past the farmhouse at a speed of v = 83 km/h. How fast is the distance between the automobile and the farmhouse increasing when the automobile is 3.1 km past the intersection of the highway and the road? Let I denote the distance between the automobile and the farmhouse, and let s denote the distance past the intersection of the highway and the road. v km/h Automobile (Use decimal notation. Give your answer to three decimal places.) speed of I at given s-value: km/h
A road perpendicular to a highway leads to a farmhouse located a = 1.3 km away. An automobile travels past the farmhouse at a speed of v = 83 km/h. How fast is the distance between the automobile and the farmhouse increasing when the automobile is 3.1 km past the intersection of the highway and the road? Let I denote the distance between the automobile and the farmhouse, and let s denote the distance past the intersection of the highway and the road. v km/h Automobile (Use decimal notation. Give your answer to three decimal places.) speed of I at given s-value: km/h
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 Description:**
A road perpendicular to a highway leads to a farmhouse located \( a = 1.3 \) km away.
An automobile travels past the farmhouse at a speed of \( v = 83 \) km/h. How fast is the distance between the automobile and the farmhouse increasing when the automobile is 3.1 km past the intersection of the highway and the road?
Let \( l \) denote the distance between the automobile and the farmhouse, and let \( s \) denote the distance past the intersection of the highway and the road.
*Note: Use decimal notation. Give your answer to three decimal places.*
**Diagram Description:**
The diagram accompanying the problem shows:
- A farmhouse located perpendicular to a highway at distance \( a = 1.3 \) km.
- An automobile traveling along the highway with a speed \( v = 83 \) km/h.
- The distance \( s \) represents how far the automobile is past the intersection of the highway and the road.
- The distance \( l \) represents the hypotenuse of the right triangle formed by \( a \) and \( s \).
**Mathematical Concept:**
To find how fast the distance \( l \) is increasing when the automobile is 3.1 km past the intersection (i.e., \( s = 3.1 \) km).
**Result Needed:**
The speed of \( l \) at a given \( s \)-value: \( \boxed{\_\_\_\_\_\_\_\_\_\_\_\_\_} \) km/h.
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