Respuesta :
The direction of the fourth displacement is θ = 12.775 ( south of west)
Explanation:
write down the values in the question,
The passage is 180m west, 290m in the direction 45° east of south, 280m at 30° east of north.
x = 290 × cos 45° + 280 × sin 30° -180
x=165.06 m
y= 280 cos ( 30° - 290 × sin (45°)
y= 37.426°
θ = tan ^-1 (y/x) = tan^-1 (37.426 / 165.06)
θ= 12.775° ( south of west)
The direction of the fourth displacement is θ = 12.775 ( south of west)
According to the question,
The surveyor travels 180m west, 290m in the direction 45° east of south, 280m at 30° east of north.
We have to calculate the x and y components of the motion.
[tex]x = 290cos 45 + 280sin 30 -180\\x = 165.06 m \\\\y= 280cos( 30 - 290sin (45)\\\\y= 37.426\\\\[/tex]
θ =[tex]tan ^-1 (y/x) = tan^-1 (37.426 / 165.06)[/tex]
θ= 12.775° ( south of west) is the required direction.
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