A particle undergoes three successive displacements in a plane, as follows: 3.50

Question

A particle undergoes three successive displacements in a plane, as follows: 3.50 m southwest, 5.00 m east, and 6.00 m in a direction 60.0° north of east. Choose the y axis pointing north and the x axis pointing east.
(a) Find the components of the first displacement.
( m ) + ( m )
Find the components of the second displacement.
( m ) + ( m )
Find the components of the third displacement.
( m ) + ( m )

(b) Find the components of the resultant displacement.
( m ) + ( m )

(c) Find the magnitude and direction of the resultant displacement.
( m ) at an angle of °

(d) Find the displacement that would be required to bring the particle back to the starting point.
( m ) + ( m ) .

Explanation / Answer

a) r1 = 3.5( -cos 45o i - sin 45o j) = -2.47 i - 2.47 j

    r2 = 5.00 i + 0 j

    r3 = 6.00 ( cos 60 i + sin 60 j) = 3.00 i + 5.20 j

b) rtot = r1 + r2 + r3 = (-2.47 i - 2.47 j) + ( 5.00 i) + ( 3.00 i +5.20 j)

    rtot = 5.53 i + 2.73 j

c) magnitude rtot = (5.532 + 2.732) = 6.17 m

   direction = tan-1(2.73/5.53) = 26.27o north of east

d) r4 + rtot = 0

   r4 = -5.53 i - 2.73 j

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