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
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter7: Exponents And Exponential Functions
Section7.8: Transforming Exponential Expressions
Problem 13PFA
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