Whenever the Connecticut River reaches a level of 105 feet above sea level, two

Question

Whenever the Connecticut River reaches a level of 105 feet above sea level, two Northampton, Massachusetts, flood control station operators begin a round-the-clock river watch. Every 2 hours, they check the height of the river, using a scale marked off in tenths of a foot, and record the data in log book. In the spring of 1996, the flood watch lasted from April 4, when the river reached 105 feet and was rising at 0.2 foot per hour, until April 25, when the level subsided again to 105 feet. Between those dates, their log shows that the river rose and fell several times, at one point coming close to the 115-foot mark. If the river had reached 115 feet, the city would have closed down Mount Tom Road (Route 5, south of Northampton). The graph below shows the rate of change of the level of the river during one portion of the flood watch. Use the graph to answer each question. (a) On what date was the river rising most rapidly? How do you know? (b) On what date was the river falling most rapidly? How do you know? (c) There were two dates in a row on which the river rose, then fell, then rose again during the course of the day. On which days did this occur, and how do you know? (d) At 1 minute past midnight, April 14, the river level was 111.0 feet. Estimate its height 24 hours later and 48 hours later. Explain how you made your estimates. (e) The river crested at 114.4 feet. On what data do you think this occurred?

Explanation / Answer

a> on 13th April from day 9 to day 10 the water level in the river was rising the most rapidly

the rate of change was = 0 - (-4.5) = 4.5 feet per day

b> on the 5th of April from day 1 to day 2 rate of change of flow = -1.5 - 2 = -3.5 feet per day

the water level fell the most rapidly.

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