A mountain climber is journeying up a mountain trail. He starts out with the sunrise, and gets to the peak just as the sun is setting. Throughout the day, he moves with inconsistent speed, slowing down to rest a few times.
He spends the night at the top, and in the morning sets out downward, reaching basecamp by nightfall. (Even though the going is easier, he stops a number of times to admire the scenery and rest.)
Is there an altitude on the mountain slope for which the climber was at that exact altitude at the same point during both days? Why or why not?
Let us Superimpose the uphill journey during the day and the downhill journey the day after so that Climber A (say) commences his journey to the top and Clumber B(say) starts his descent from the top at the same instant. we observe that the respective speeds of both the climbers must be equal , since the jouneys of A and B, in reality are the superimposed journeys of the same person at different time periods.
Consequently, it follows that thre must exist an altitude (or point) on the mountain slope for which the climber was at that exact altitude at the same point during both days.
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