Climbing the Glacier

Joe Alpine stands at the base of the Flugelhorn Glacier, a long, tilted slab of ice and snow. His guide tells him that the top of the formation lies 500 meters above their current location. "Be careful," warns the guide, "it's really slippery."

"Hah!" snorts Joe. "My boots and ice axe will make short work of this obstacle. Once I set my mind to a task, I don't give up!"

Joe starts climbing. Every now and then, however, he slips and slides backward, down the face of the ice. True to his word, as soon as he recovers his footing, he heads up again. Over the next hour, the guide tries to measure Joe's progress -- but since there are few markings on the snow, his estimates have large uncertainties.



      climb    150  +/-  10  meters
      slip      80  +/-  40  meters
      climb     60  +/-  10  meters
      slip     100  +/-  50  meters
      climb    180  +/-  10  meters
      slip      70  +/-  40  meters
      climb    210  +/-  20  meters

Based on the guide's measurements,

How far above the base of the glacier is Joe now? Be sure to include an uncertainty in your answer.
Re-write your result with the appropriate number of significant digits.
Has Joe reached the top of the glacier?

Real alpine climbing is no joke.

The North Face of the Eiger has challenged climbers for over a century.
A fatal accident in 2009