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A grasshopper makes four jumps. The displacement vectors are (1) 35.0 cm, due west; (2) 25.0...

A grasshopper makes four jumps. The displacement vectors are (1) 35.0 cm, due west; (2) 25.0 cm, 34.0 ° south of west; (3) 21.0 cm, 61.0 ° south of east; and (4) 18.0 cm, 55.0 ° north of east. Find (a) the magnitude and (b) direction of the resultant displacement. Express the direction as a positive angle with respect to due west.

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Answer #1

net horizontal displacement

dx = - 35 - 25 cos 34 + 21 cos 61 + 18 cos 55

dx = - 35.22 cm

net vertical displacement

dy = - 25 sin 34- 21 sin 61 + 17 sin 55

dy = - 17.6 cm

======

net displacement

d^2 = dx^2 + dy^2

d = 39.374 cm

direction

x = arcran ( dy/dx) = 26.552 south of west

=======

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