1. They are all different people, except just with the same faces. Emar is one of the boys in the building. He is on the second floor at the very top of the stairway to the first floor. The horizontal distance between the floors is 20 m. The slope of the stairway is defined by the equation y=(-8/31)x + 8. Because Emar is nervous, he begins to walk fully up and down the stairway continuously. As he walks, his height from his feet to the outside ground follow a sinosoidal pattern. On average, it takes him 75 seconds to get from one floor to the other. He begins to walk 2.5 minutes before the first selection is made.

2. a) Determine the equation of his height from his feet to the outside ground in terms of sine. Note that the building has a base that is 1 m. thick. Use seconds for your unit of time and meters for your unit of height. Assume that the point where Emar is standing has an x-coordinate of 0.5. Neglect 2:35 PM in your graph if you create one. The starting point is instead zero seconds. b) Assume Sophia, a girl, was already on the stairway before Emar began to walk. The horizontal distance between Emar and Sophia is 3.13 m. If she moves at a velocity of 14.3 m. every 75 seconds down the stairs, at what height will the two be at the same spot? c) How many possible combinations of selected people are there if the time is 2:49 PM?