You aren’t going to be using any Calc III calculating, just a bit of trig and algebra, oh and some vector notation. The lines of equal elevation are marked and labeled in grey. They are given every 100 ft on this particular map. A scale is given on the right, with units in both miles and kilometers.

1.

 a) Standing on top of the mountain (black triangle), what is the direction vector with the steepest slope from the peak to the 2500’ level?

 b) What is the average slope in that direction? (Be careful of units!) And what is your average angle of descent?

c) If the slope were constant and the trail straight in that direction (if there was a trail) what would the length of the trail be?

2.

 a) Going from the peak to the 3000’ level, in which direction is the slope the least steep? Mark that point ‘a’.

b) From point a, in which direction is it least steep to get to the 2900’ level? Mark that point ‘b’.

c) From point b, in which direction is it least steep to get to the 2800’ level? Mark that point ‘c’.

d) If you were going all the way from the peak directly to the 2800’ level (i.e. traveling in a straight line), in which direction is it the least steep? Mark that point ‘d’.

e) Are points ‘c’ and ‘d’ in the same place? If so, do you think this would always be the case? Can you illustrate your assertion?

3. Along which trail – Marlboro, Dublin, Pumpelly, White Arrow, or White Cross – is the trail steepest in going from 2900 ft to 2500 ft?

 4. Which trail has uphill stretches (a rise of at least 100 ft) even as you are making your descent?

 5. What is the approximate change in elevation if you go from the peak and head due North for 1 kilometer?