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A drunken sailor stumbles 535 meters north, 485 meters northeast, then 435 meters northwest.?
A drunken sailor stumbles 535 meters north, 485 meters northeast, then 435 meters northwest. What is the total displacement and the angle of the displacement? (Assume east is the +x-direction and north is the +y-direction.)
magnitude: _____
direction: _____ degrees counter-clockwise from the +x-axis
1 Answer
- kuiperbelt2003Lv 710 years agoFavorite Answer
find the components of each leg:
a) 535 north
b)485 northeast = 485cos 45 east and 485 sin 45 north = 343m east and 343 m north
c) 435 northwest = 308 m north and 308 m west
add components:
total north displacement = 1186m
total east/west displacement = 343+(-308)=35m
magnitude of final displacement = sqrt[1186^2+35^2]=1186.5m
tan(theta)=north displacement/east displacement = 1186/35=33.9=>
theta=arctan(33.9)=88.3 deg
