A small object undergoes three displacements that return it to thestarting point

Question

A small object undergoes three displacements that return it to thestarting point. In the
first displacement, the object moves 1.00m at an angle of 60degrees east of north. It travel on
an unknown second displacement. The final displacement is1.69m along a direction
17.2 degrees north of west. What was the second displacement,giving both magnitude and
compass direction?

Explanation / Answer

A small object undergoes three displacements that return it to thestarting point. In the first displacement, the object moves 1.00m at an angle of 60degrees east of north. It travel on an unknown second displacement. The final displacement is1.69m along a direction 17.2 degrees north of west. What was the second displacement,giving both magnitude and compass direction? as the total displacement is zero the sum of x components of individualdisplacements    =    0 also the sum of Y component of individual displacements =0 X=1.00sin60+1.69sin17.2+x component of seconddisplacement=0 so X component of second displacement=-(0.8660+0.4997)=-1.3657m Y=1.00cos60+1.69cos17.2+y component of seconddisplacement=0 Y component of second displacement=-(0.5+1.6144)=-2.1144m the resultant of seconddisplacement=1.8651+4.4706=2.5170 direction =tan-1(2.1144/1.3657)=> =57.14degree it is in the third quadrant . hence the second displacement is 2.5170m along adirection 57.14 degrees south of west.

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