Question: The Spider and the Bug (a pursuit problem) Initially a bug is at the origin, and a spider is at position (1,0). The bug begins

The Spider and the Bug (a pursuit problem)

Initially a bug is at the origin, and a spider is at position (1,0). The bug begins moving up the y-axis at unit speed, and the spider immediately pursues the bug at speed k, always moving directly towards the bug.

Questions:

1. (a) If the spider desires to catch the bug at (0,1), what will be the spider's speed?

(b) What distance does the spider cover if the bug is caught at (0,1)?

2. If the spider's speed is the same as the bug's ( k = 1 ), then the spider will be forever trailing the bug. At what limiting distance behind the bug?

The Spider and the Bug (a pursuit problem)

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