You are on a treasure hunt and your map says "Walk due west for
58.0 paces, then walk 30.0° north of west for 40.4 paces, and
finally walk due north for 19.8 paces." What is the magnitude of
the component of your displacement in the
direction (a) due north
and (b) due west?
(a)
Number
Units
paces
(b)
Number
Units
paces
Two bicyclists, starting at the same place, are riding toward
the same campground by different routes. One cyclist rides 1060 m
due east and then turns due north and travels another 1500 m before
reaching the campground. The second cyclist starts out by heading
due north for 1900 m and then turns and heads directly toward the
campground. (a) At the turning point,
how far is the second cyclist from the
campground? (b) In what direction
(measured relative to due east within the range (-180°, 180°]) must
the second cyclist head during the last part of the trip?
(a)
Number
Units
m
(b)
Number
Units
°
A sailboat race course consists of four legs, defined by the
displacement vectors A, B, C, and D,
as the drawing indicates. The magnitudes of the first three vectors
are A = 3.70 km, B = 5.10 km,
and C = 4.70 km. The finish line of the course
coincides with the starting line. Using the data in the drawing,
find (a) the distance of the fourth leg
and (b) the angle θ.
(a)
Number
Units
km
(b)
Number
Units
°
Two geological field teams are working in a remote area. A
global positioning system (GPS) tracker at their base camp shows
the location of the first team as 44 km away, 23° north of west,
and the second team as 31 km away, 30° east of north. When the
first team uses its GPS to check the position of the second team,
what does it give for the second
team's (a) distance from them
and (b) direction, measured from due
east?
(a) Number Units
km
(b) Number Units
°
Multiple Concept Example 9 provides background pertinent to
this problem. The magnitudes of the four displacement vectors shown
in the drawing are A = 14.0 m, B = 11.0 m, C = 11.0 m,
and D = 27.0 m. Determine
the (a) magnitude
and (b) direction for the resultant that
occurs when these vectors are added together. Specify the direction
as a positive (counterclockwise) angle from the
+x axis.
(a)
Number
Units
m
(b)
Number
Units
°