Final answer:
To determine the speed of the brick just before it reaches the bottom of the roof, we can use the principle of conservation of energy. The potential energy of the brick at point A is equal to the kinetic energy just before it reaches the bottom. Using this principle, we can calculate that the speed of the brick just before it reaches the bottom is 8 ft/s.
Step-by-step explanation:
To determine the speed of the brick just before it reaches the bottom, we can use the principle of conservation of energy. The potential energy of the brick at point A is given by mgh, where m is the mass of the brick, g is the acceleration due to gravity, and h is the height of point A above the bottom. The kinetic energy of the brick just before it reaches the bottom is given by (1/2)mv^2, where v is its velocity. Since the roof is smooth, there is no loss of energy due to friction. Therefore, the potential energy at point A is equal to the kinetic energy just before the brick reaches the bottom.
Let's assume that the height of point A above the bottom is h. The potential energy at point A is given by mgh = (2 lb)(32.2 ft/s^2)(h). The kinetic energy just before the brick reaches the bottom is given by (1/2)mv^2 = (1/2)(2 lb)v^2 = v^2 lb-ft/s^2.
Since the potential energy at point A is equal to the kinetic energy just before the brick reaches the bottom, we can equate the two expressions: (2 lb)(32.2 ft/s^2)(h) = v^2 lb-ft/s^2. Solving for v, we get v = sqrt((2 lb)(32.2 ft/s^2)(h)/lb-ft/s^2) = sqrt(64.4h ft/s^2) = 8ft/s.