1. A streetlight is on top of a pole 4 meters high. A person 1.8 meters tall is 6 meters from the base of the pole and is walking directly toward the pole at a constant rate of 2 meters per second. (a) At what rate is the person's shadow shortening? (b) At what rate is the tip of the person's shadow moving? 2. At 2:00 P.M. a ship, which is steaming north at 20 knots, is 4 nautical miles west of a lighthouse. At the same time, a motor launch, traVeling 10 knots, is proceeding south from a point 4 nautical miles east of the lighthouse. Find the rate of change of the distance between the ship and the launch at 3:30 P.M., assuming that they maintain their respective speeds and courses. 3. A girl on a bike rides north 8 kilometers and then turns east. If she rides at a steady rate of 16 kilometers per hour, at what rate is the distance, measured directly between the girl and her starting point, changing 2 hours after she leaves that point? 4. A ladder 4 meters long is leaning against the vertical wall of a house. If the base of the ladder is pulled horizontally away from the house at the rate of 0.7 meter per second, how fast is the top of the ladder sliding down the wall at the instant when it is 2 meters from the ground? 5. Sand is falling at the rate of 2 cubic meters per minute upon the tip of a sandpile, which maintains the form of a right circular cone whose height is the same as the radius of the base. Find the rate at which the height of the pile is increasing at the instant when the pile is 6 meters high