1. A ladder 15 ft long rests against a vertical wall. Its top slides down the wall while its bottom moves away along the level ground at a speed of 2 ft/s. How fast is the angle between the top of the ladder and the wall changing when the angle is ?/3 radians? 2. A ladder 12 meters long leans against a wall. The foot of the ladder is pulled away from the wall at the rate 1 2 m/min. At what rate is the top of the ladder falling when the foot of the ladder is 4 meters from the wall? 3. A rocket R is launched vertically and its tracked from a radar station S which is 4 miles away from the launch site at the same height above sea level. At a certain instant after launch, R is 5 miles away from S and the distance from R to S is increasing at a rate of 3600 miles per hour. Compute the vertical speed v of the rocket at this instant. 4. A boat is pulled into a dock by means of a rope attached to a pulley on the dock, Figure 2.1. The rope is attached to the bow of the boat at a point 1 m below the pulley. If the rope is pulled through the pulley at a rate of 1 m/sec, at what rate will the boat be approaching the dock when 10 m of rope is out.