An adjustable exercise bench shown in the picture, schematic and vector model. In this bench, the adjustment holes are on the rear bench leg $($ r $1).$ You need to determine the velocity of the bench components based on the rate at which the back of the bench is rotated $($omega$\_2).$ All Units are $\backslash (\backslash$mathrm$\{$cm$\},\backslash$mathrm$\{$cm$\}/\backslash$mathrm$\{$s$\}\backslash ),$ radians, radians $\backslash (/\backslash$mathrm$\{$s$\}\backslash )$

Solve for Vpy$\_($y component of of vector Vp$.$ velocity of point P$)$: Use the method covered in class.

Assume that the angular velocity of the bench $($omega$\_2)$ is given.

Given data is here and on figure and table. $\backslash (\backslash$mathrm$\{$r$1\}=122\backslash )$; theta$1\backslash (=2\mathrm{.}7053$ ; $\backslash$mathrm$\{$r$\}2=69\backslash )$; theta$\_2=0\mathrm{.}5237$; omega$\_2=1\mathrm{.}4$; r$3=105$; t$3=2\mathrm{.}1816$; r$2$P $=100$;