While exploring a cave, a spelunker starts at the entrance and moves the followi

Question

While exploring a cave, a spelunker starts at the entrance and moves the following distances. She goes 75.0 m north, 250 m east, 113 m at an angle 30.0degree north of east, and 191 m south. Find the resultant displacement from the cave entrance. The figure below suggests the situation but is not drawn to scale. Use the component method to add the vectors A and B shown in the figure. Both vectors have magnitudes of 3.20 m end vector A makes sn angle of theta = 35.5degree with the x axis Express the resultant A + B m unit-vector notation.

Explanation / Answer

Let the North be positive y and East be positive x direction

d1 = 75 y
d2 = 250 x
d3=113 cos 30 x + 113 sin 30 y
= 97.9 x + 56.5 y
d4 = -191 y

d = d1 + d2 + d3 + d4
= 75 y + 250 x + 97.9 x + 56.5 y - 191 y
= 347.9 x - 59.5 y

magnitude = sqrt (347.9^2 + 59.5^2)
= 353 m

It lies south east direction
angle = atan (59.5/347.9)
= 9.7 degree

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