121616949-math.140

# 121616949-math.140 - 126 Chapter 6 Applications of the...

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126 Chapter 6 Applications of the Derivative . . . . . . . . . . . . . . Figure 6.14 Falling ball. 19. Do example 6.18 assuming that the angle between the two roads is 120 instead of 90 (that is, the “north–south” road actually goes in a somewhat northwesterly direction from P ). Recall the law of cosines: c 2 = a 2 + b 2 - 2 ab cos θ . 20. Do example 6.18 assuming that car A is 300 meters north of P , car B is 400 meters east of P , both cars are going at constant speed toward P , and the two cars will collide in 10 seconds. 21. Do example 6.18 assuming that 8 seconds ago car A started from rest at P and has been picking up speed at the steady rate of 5 m/sec 2 , and 6 seconds after car A started car B passed P moving east at constant speed 60 m/sec. 22. Referring again to example 6.18 , suppose that instead of car B an airplane is flying at speed 200 km/hr to the east of P at an altitude of 2 km, as depicted in figure 6.15 . How fast is the distance between car and airplane changing? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A B c ( t ) . . . . Figure 6.15 Car and airplane.
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Unformatted text preview: . . . . . . . . . Figure 6.15 Car and airplane. 23. Referring again to example 6.18 , suppose that instead of car B an airplane is ﬂying at speed 200 km/hr to the east of P at an altitude of 2 km, and that it is gaining altitude at 10 km/hr. How fast is the distance between car and airplane changing? ⇒ 24. A light shines from the top of a pole 20 m high. An object is dropped from the same height from a point 10 m away, so that its height at time t seconds is h ( t ) = 20-9 . 8 t 2 / 2. How fast is the object’s shadow moving on the ground one second later? ⇒ 25. The two blades of a pair of scissors are fastened at the point A . Let a denote the distance from A to the tip of the blade (the point B ). Let β denote the angle at the tip of the blade that is formed by the line AB and the bottom edge of the blade, line BC , and let θ denote the angle between AB and the horizontal. Suppose that a piece of paper is cut in such a...
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