A person going for a walk follows the path shown in Figure P1.47 where y 1 = 290

Question

A person going for a walk follows the path shown in Figure P1.47 where y1 = 290 m and = 64.0°. The total trip consists of four straight-line paths. At the end of the walk, what is the person's resultant displacement measured from the starting point?
m
° (from the +x axis)

A person going for a walk follows the path shown in Figure P1.47 where y1 = 290 m and theta = 64.0degree. The total trip consists of four straight-line paths. At the end of the walk, what is the person's resultant displacement measured from the starting point? m degree (from the +x axis)

Explanation / Answer

we can find the final position vector,
for the X components ,
final value of X coordinate = +100 + 0 - 150 cos 30 - 200 cos = +100 + 0 - 150 cos 30 - 200 cos 64

= -117.5

final value of Y coordinate = 0 - y1 - 150 sin 30 + 200 sin =  0 - 290 - 150 sin 30 + 200 sin 64= -185.2 ;

hence the displacement vector is   -117.5 i - 185.2 j ;

hence displacement is = ( 117.5^2 + 185.2^2 ) = 219. 3 form the origin.

angle w r t +ve X axis = tan inv ( - 185.2 / -117.5 ) = 57.6 deg ,

since both componenents are in 3rd quadrant , so

angle = 57 .6 -180 = -122 degree from + ve X axis

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