If you look at a circular disk, such as a quarter, head on, you see a circle. But if you
Chapter 14, Problem 14.3.22(choose chapter or problem)
If you look at a circular disk, such as a quarter, head on, you see a circle. But if you tilt the disk away from your line of sight, as shown in Figure 14.24, the disk appears elliptical. The length of the apparent ellipses horizontal axis does not change, but the length of the vertical axis decreases. (a) Find a formula for , the length of the ellipses vertical axis, in terms of , the angle of tilt with respect to the line of sight. (b) What does your formula say about the appearance of the coin after being tilted through an angle of = 0? = 90? = 180? Does this make sense? (c) Find a formula for the ellipse formed by tilting a disk of radius r through an angle of . Assume that the disk is centered at the origin and that the disk is being titled around the x-axis, so that the length of its horizontal axis does not change. (d) The equation x2/16 + y2/7=1 describes an ellipse. If we think of this ellipse as a tilted disk, then what is the disks radius, and through what angle has it been tilted?
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