In the movie The Drowning Pool, private detective Lew Harper (played by Paul Newman) is trapped by the bad guy in a room containing a swimming pool. The room may be considered rectangular, 5 meters wide by 15 meters long, with an open skylight window 10 meters above the floor. There is a single entry to the room, reached by a stairway; a locked 2-m high by 1-m wide door, whose bottom is 1 meter above the floor. Harper knows that his energy will return in eight hours and decides he can escape by filling the room with water and floating up to the skylight. He plugs the drain with his clothes, turns on the water valves, and prepares to put his plan into action.

(a) Prove that if the door is completely under water and h is the distance from the top of the door to the surface of the water, then the net force exerted on the door satisfies the inequality F > pH2OghAdoor

(Don’t forget that a pressure is also exerted on the door by the outside air.)

(b) Assume that water enters the room at about five times the rate at which it enters an average bathtub and that the door can withstand a maximum force of 4500 Newton’s (about 1000lbf). Estimate (i) whether the door will break before the room fills and (ii) whether Harper has time to escape if the door holds. State any assumptions you make.