A vertical curve crosses a 4-ft diameter pipe at right angles. This pipe is located at station 110+85 and its center, where it crosses the road, is at elevation 1091.60ft. The PVI of the vertical curve is at station 110+00 and elevation 1098.4ft. The vertical curve is 600ft long and connects an initial grade of 1.2% and a final grade of -1.08%. Determine the depth, below the surface of the curve, of the top of the pipe and determine the station of the highest point on the curve. Does the curve in provide sufficient stopping sight distance for a speed of 60mph? Assume a deceleration rate of 11.2ft/sec2.

To save energy, the air supply to a 2000 ft office has been shut off overnight and the room temperature has dropped to 40°f. in the morning, the thermostat is reset to 70°f and warm air at 120 f begins to flov in at 200ft'/min. the air is well mixed within the room, and an equal mass flow of air at room temperature (changing with time) is withdrawn through a return duct. the air pressure is nearly 1 atm everywhere. ignoring heat transfer with the surroundings and kinetic and potential energy effects, estimate how long it takes for the room temperature to reach 70°f. plot the room temperature as a function of time.