Physics

There was once an episode of Lassie in which the dramatic conclusion found Timmy (or whatever was the name of Lassie’s boy-companion) stranded on an island in a river with flood waters rising rapidly. Of course, Lassie jumped into the raging torrent without a moment’s hesitation, swam across and struggled back with Timmy clinging grimly to her collar. After which they all went home for hot cocoa and dog biscuits, while we went to a commercial break. For this problem assume that the raging river is flowing with a speed of 10 m/s, that Lassie can swim (in still water) at a speed of 1 m/s and that the island is separated from the bank of the river by 10 m. a Not knowing anything about Galilean velocity transformations, Lassie points her nose at Timmy, directly across the river, and starts swimming. What direction does her velocity vector point as observed by Timmy’s parents, standing on the bank of the river? What direction does her velocity vector point as observed by a fish floating in the raging river? What are the two frames of reference and the object here? b How far down the island does Lassie end up if she swims blindly as described above? How long does it take her to cross the river? c Can Lassie swim at an angle to the current so that she ends up going straight across the river? What about Aquaman, who can swim at a speed of 20 m/s in still water? d How would the above problem differ if Lassie were a beam of light, emmitted by a flashlight, floating in the river. You don’t have to give a numerical answer for this problem, just discuss how the beam of light behaves differently than Lassie when transforming between reference frames.

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