HL Unit 1, Day 3: Related Rates
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Figure 1.4: From [3]
an eastbound train traveling at 80 meters per second. At how many meters per second is the train moving away from the observer 3 seconds after it passes through the intersection? [Ans: 76.8] 1.C-5 (from HL 11/03) An airplane is flying at a constant speed at a constant altitude of 3 km in a straight line that will take it directly over an observer at ground level. At at given instant the observer notes that the angle θ is 1 1 π radians and is increasing at radians per second. Find the speed, in 3 60 kilometers per hour, at which the airplane is moving towards the observer. 1 Ans: 15 km/s = 240 km/hr Figure 1.5: Airplane flying towards an observer.
1.C-6 Figure 1.6 shows an isosceles triangle ABC with AB = 10 cm and AC = BC. The vertex C is moving in a direction perpendicular to (AB) with speed 2 cm per second. Calculate the rate of of the angle CAB increase 1 at the moment the triangle is equilateral. Ans: 10 radians per second 1.C-7 (adapted from D&S) Two cars start at the same place and at the same time. One car travels east at a constant velocity of 40 miles per hour and a second car travels north at a constant velocity of 48 miles per hour. Approximately how fast is the distance between them changing after half an hour? Round your answer to the nearest mile per hour. [Ans: 62 mph] Mr. Budd, compiled September 29, 2010