1. A flat, steel plank is leaning against a wall. The plank is 41 feet long. The wall itself is flat and perpendicular to a flat floor. The top of the plank is initially touching the wall at a point 39 feet above the floor. The top of the plank starts to slide down, without leaving the wall, at a constant rate of 5 feet per minute. The bottom of the plank never leaves the floor. (a) At the six minute mark, what is the speed of the lower end? (b) At the six minute mark, at what rate is the angle the plank makes with the floor changing? 2. A 15 foot ladder leans against a vertical wall. If the top slides down- ward at the rate of 2 ft/sec, find the speed of the lower end when it is 12 feet from the wall. 3. A lighthouse that is half a mile west of shore has a rotating light that makes 2 revolutions per minute in the counterclockwise direction. The shoreline runs north-south, and there is a cave on the shore directly east of the lighthouse. How fast is the beam of light moving along the shore at a point 1 mile north of the cave? 4. A spherical snowball evaporates at a rate proportional to its surface area. Show that its radius shrinks at a constant rate