While exploring a cave, a spelunker starts at the entrance andmoves the followin
ID: 1680345 • Letter: W
Question
While exploring a cave, a spelunker starts at the entrance andmoves the following distances: 75.0 m north, 250 m east, 170 m atan angle 30.0° north of east, and 150 m south.Find the resultant displacement from the cave entrance and thedirection it is in (degrees)
While exploring a cave, a spelunker starts at the entrance andmoves the following distances: 75.0 m north, 250 m east, 170 m atan angle 30.0° north of east, and 150 m south.
Find the resultant displacement from the cave entrance and thedirection it is in (degrees)
Explanation / Answer
the x and y components of 170m 30deg north of east is: x = 170cos30 = 147.22meast y = 170sin30 = 85mnorth therefore the total x and y displacements are: X-direction : 147.22m + 250m = 397.22m east Y- direction : 85m + 75.0m - 150m = 10m north Therefore the resultant displacement is: R =[(397.22m)2+(10m)2] = 397.345m The resultant angle is: = arctan(y/x) = arctan (10/397.22) = 1.442degrees north of east
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