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?
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?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F86312609-a27e-4f25-b5c2-0d6affa207a5%2Fdf7a0007-8020-4d63-9987-9c271bbb00d4%2F1rpuqcf_processed.jpeg&w=3840&q=75)
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
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