1. A man walks along a straight path at a speed of π ft/s. Asearchlight is located on the ground 18 ft from the path and iskept focused on the man. At what rate is the searchlight rotatingwhen the man is 30 ft from the searchlight? Draw a picture first tounderstand the problem.
2. Suppose square ABCD has straight edges of length 2, and itscorners are connected by hinges. When pulling corners A and C, thesquare slowly deforms into a rhombus. Given that the area A of arhombus can be expressed as A = 2a2 sinθ, where θ is oneof the angles of the rhombus, and a is the side length, find therate of change of the area when one of the angles of the rhombus isπ/3 rad, and it is also decreasing at a rate of π/12 rad/s.
