The Weather Monitor. Your South American
expedition splits into two groups: one that stays at home base, and
yours that goes off to set up a sensor that will monitor
precipitation, temperature, and sunlight through the upcoming
winter. The sensor must link up to a central communications system
at base camp that simultaneously uploads the data from numerous
sensors to a satellite. In order to set up and calibrate the
sensor, you will have to communicate with base camp to give them
specific location information. Unfortunately, the group’s
communication and navigation equipment has dwindled to
walkie-talkies and a compass due to a river-raft mishap, which
means your group must not exceed the range of the walkie-talkies
(3.0 miles). However, you do have a laser rangefinder to help you
measure distances as you navigate with the compass. After a few
hours of hiking, you find the perfect plateau on which to mount the
sensor. You have carefully mapped your path from base camp around
lakes and other obstacles: 580 m West (W), 280 m S, 770 m W, 940 m
NE, 870 m W, and 420 m 30.0° W of S. The final leg is due south,
2.50 km up a constant slope and ending at a plateau that is
h = 310 m above the level of base camp.
(a) How far are you from base camp? Will you be
able to communicate with home base using the walkie-talkies?
(b) What is the geographical direction from base
camp to the sensor (expressed in the form θ° south of
west, etc.)?
(c) What is the angle of inclination from base
camp to the detector?
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