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Courtesy of Alar Toomre, Massachusetts Institute of Technology One day it began to snow exactly at noon at a heavy and steady rate. A snowplow left its garage at 1:00 P.M., and another one followed in its tracks at 2:00 P.M. (see Figure 2.15 on page 85). (a) At what time did the second snowplow crash into the first? To answer this question, assume as in Project D that the rate (in mph) at which a snowplow can clear the road is inversely proportional to the depth of the snow (and hence to the time elapsed since the road was clear of snow). [Hint: Begin by writing differential equations for x(1) and y(t), the distances traveled by the first and second snowplows, respectively, at t hours past noon. To solve the differential equation involving y, let t rather than y be the dependent variable!] (b) Could the crash have been avoided by dispatching the second snowplow at 3:00 P.M. instead? Projects for Chapter 2 85 y(1) Figure 2.15 Method of successive snowplows x(1) Miles from garage

Courtesy of Alar Toomre, Massachusetts Institute of Technology One day it began to snow exactly at noon at a heavy and steady rate. A snowplow left its garage at 1:00 P.M., and another one followed in its tracks at 2:00 P.M. (see Figure 2.15 on page 85). (a) At what time did the second snowplow crash into the first? To answer this question, assume as in Project D that the rate (in mph) at which a snowplow can clear the road is inversely proportional to the depth of the snow (and hence to the time elapsed since the road was clear of snow). [Hint: Begin by writing differential equations for x(1) and y(t), the distances traveled by the first and second snowplows, respectively, at t hours past noon. To solve the differential equation involving y, let t rather than y be the dependent variable!] (b) Could the crash have been avoided by dispatching the second snowplow at 3:00 P.M. instead? Projects for Chapter 2 85 y(1) Figure 2.15 Method of successive snowplows x(1) Miles from garage

Advanced Engineering Mathematics
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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E Two Snowplows Courtesy of Alar Toomre, Massachusetts Institute of Technology One day it began to snow exactly at noon at a heavy and steady rate. A snowplow left its garage at 1:00 P.M., and another one followed in its tracks at 2:00 P.M. (see Figure 2.15 on page 85). (a) At what time did the second snowplow crash into the first? To answer this question, assume as in Project D that the rate (in mph) at which a snowplow can clear the road is inversely proportional to the depth of the snow (and hence to the time elapsed since the road was clear of snow). [Hint: Begin by writing differential equations for x(t) and y(t), the distances traveled by the first and second snowplows, respectively, at t hours past noon. To solve the differential equation involving y, let t rather than y be the dependent variable!] (b) Could the crash have been avoided by dispatching the second snowplow at 3:00 P.M. instead? 0 Projects for Chapter 2 85 y(t) Figure 2.15 Method of successive snowplows x(t) Miles from garage
Transcribed Image Text:E Two Snowplows Courtesy of Alar Toomre, Massachusetts Institute of Technology One day it began to snow exactly at noon at a heavy and steady rate. A snowplow left its garage at 1:00 P.M., and another one followed in its tracks at 2:00 P.M. (see Figure 2.15 on page 85). (a) At what time did the second snowplow crash into the first? To answer this question, assume as in Project D that the rate (in mph) at which a snowplow can clear the road is inversely proportional to the depth of the snow (and hence to the time elapsed since the road was clear of snow). [Hint: Begin by writing differential equations for x(t) and y(t), the distances traveled by the first and second snowplows, respectively, at t hours past noon. To solve the differential equation involving y, let t rather than y be the dependent variable!] (b) Could the crash have been avoided by dispatching the second snowplow at 3:00 P.M. instead? 0 Projects for Chapter 2 85 y(t) Figure 2.15 Method of successive snowplows x(t) Miles from garage
- n(t) = n(t-1) + (1/12) t-1 3 Thus, at the time the second snowplow crashed into the first one is t that satisfies equation (3). To calculate the exact time we will be needing more information. = Step 4: For (b), The answer to "Could the crash have been avoided by dispatching the second snowplow at 3.00 pm instead?" depends on the values of c₁ and C2. So, for example if = then the crash happens C2 when t = 4. Note: For more accurate answers we will be needing more information. Solution (a) At the time the second snowplow crashed into the first one is t that satisfies equation (3). (b) The answer to "Could the crash have been avoided by dispatching the second snowplow at 3.00 pm instead?" depends on the values of c₁ and C2. WAS THIS HELPFUL?
Transcribed Image Text:- n(t) = n(t-1) + (1/12) t-1 3 Thus, at the time the second snowplow crashed into the first one is t that satisfies equation (3). To calculate the exact time we will be needing more information. = Step 4: For (b), The answer to "Could the crash have been avoided by dispatching the second snowplow at 3.00 pm instead?" depends on the values of c₁ and C2. So, for example if = then the crash happens C2 when t = 4. Note: For more accurate answers we will be needing more information. Solution (a) At the time the second snowplow crashed into the first one is t that satisfies equation (3). (b) The answer to "Could the crash have been avoided by dispatching the second snowplow at 3.00 pm instead?" depends on the values of c₁ and C2. WAS THIS HELPFUL?
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