Three forces acting on a body are shown in the figure. To have the resultant force only along the y -direction, the magnitude of the minimum additional force needed is

Step-by-step solution

Minimum additional force needed aligned & F=- (F_ resultant )_x & F_ resultant =[(4-2)( 30 j - 30 i ) = & [2 ( 3 2 j - 1 2 i )+ ( 1 2 i + 3 2 j ) ] = & [ ( 3 + 3 2 ) j + 60 j ) = & . [- 1 2 i + 3 3 2 i + i 2 ) ] = & - i 2 + 3 3 2 j F=- (- i 2 )= 1 2 i aligned Hence, |F|=0.5 ~N