Two Snowplows: One day it began to snow exactly at noon at a heavy and steady...

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Advance Math

Two Snowplows: One day it began to snow exactly at noon at aheavy and steady rate. A snow plow left its garage at 1:00 pm, andanother followed in its tracks at 2:00 pm. (a) At what time did thesecond snowplow crash into the first? To answer this questions,assume as in Project D that the rate (in mph) at which a snowplowcan clear the road is inversely proportional to the depth fo thesnow (and hence to the time elapsed since the road was clear ofsnow). [Hint: Begin by writing dierential equations for x(t) andy(t), the distances traveled by the first and second snowplows,respectively, at t hours past noon. To solve the dierentialequation involving y, let t rather than y be the dependentvariable!]
(b) Could the crash have been avoided by dispatching the secondsnowplow at 3:00 pm instead?
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4.3 Ratings (705 Votes)

Let midday be t 0 in hours and let the first and secondsnowplows cover distances xt and yt by time t Then the firstsnowplow starts at t1 and the second at time t2The distance covered by the first snowplow follows an equationof the formwhere h1t is the height of snow in front of thesnowplow at time t It is clear that since the snow startedfalling at middayFor some constant rate of fall of snow r in appropriate unitsHencewhere kr See Answer

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