3. A streetlight is 6 meters above the ground. A person who is 1.5m tall is currently standing an unknown distance away from the streetlight and casting a shadow along the ground. The person starts wallking toward the streetlight at a rate of 1m/s. How fast is the length of the shadow shrinking? Does it depend on how far the person is standing from the streetlight? (a) Draw a diagram showing the situation. (Similar triangles are involved.) (b) Using related rates, determine how fast the length of the person's shadow is shrinking. (Hint: Let x be the distance that the person is from the streetlight, and s be the length of the person's shadow. Use similar triangles to set up an equation between ¤ and s.) Give your answer as a concluding sentence, with correct units. Note: It is possible to get the answer without knowing the distance the person is standing. The answer does not depend on the current value of T.

You are standing 12 feet away from a balloon launcher that will release a balloon vertically up into the air at a raise of 2 ft/sec. When the balloon is 10 feet up in the air, at what rate is the angle changing between the horizontal and the line of sight?

15. A hot-air balloon is rising straight up at 5 ft/sec. An observation area is located 80 feet from the take-off point. At the moment that the balloon reaches a height of 60 feet: (a) How fast (in radians/sec) is the angle of elevation from the observation area to the balloon changing? (b) How fast is the distance between the observation area and the balloon changing?

Consider a triangle where two sides have fixed lengths 14 cm and 16 cm. Suppose the two sides are initially at an angle of a = and that they are closing together so that the angle between them is decreasing at a rate of radians per second. What is the rate at which the area of the triangle is decreasing when a = "? 16 cm?/s