Why solution assume vca vcacos45ivcasin45j why this assume

Why solution assume v(c/a) = v(c/a)cos45i+v(c/a)sin45j ???

why this assume is wrong? [v(c/a)= w x r(c/a) so that -v(c/a)cos45i + v(c/a)sin45j ]

other problems is solved by v(rel) = w x r(rel) , a(rel) = angular acceleration x r(rel) -w^2r(rel)

16-130. Rod AB rotates counterclockwise with constant angular velocity a Determine the velocity and acceleration of point Clocated on the double collar when at the position shown. The collar consists of two pin-connected slider blocks which are constrained to move along the circular path and the rod AB. 3 rad o 45 r 04 m deg Given: Solution Guesses are/ 1 vrei act Given sin(26) cos (6) (0) r rcos (20 vc cos (20) rel Sin 6) 0 x sin(20) sin(20) cos (0) r rcos (20 2 -cos (20 acr cos (20 VC -sin 2 rel sin (0) 0 x 0 x rsin(20) cos (0) 2 0 x vrei sin(0) vrel arel) (-5.09) m vrel (-1.70 m Find vrel, arei, VC,act 2.40 s 0.00 2

Solution

Answer: 1) velocity of point c with respect to a

here v(c/a)cos 45 is the horizontal component and v(c/a)sin 45 is the vertical component

and according to vector equation U =ui+vj,

so, v(c/a) = v(c/a)cos 45 i + v(c/a)sin 45 j

2) since horizontal component is going in negative zone towards left so horizontal component is negative and vertical component is going up so v(c/a) = v(c/a)cos 45 i + v(c/a)sin 45 j

v(rel) = w*r(rel)

r(rel) = v(rel) / w

a(rel) = ang acceleration*r(rel) - w²r(rel)