Problem $1[18$ pts$]$: Using PVA analysis

Consider the mechanism drawn below. The goal is to algebraically determine the velocity, position, and acceleration at point P using PVA analysis. Assume the following:

$O2=(0,0),O4=(10,0),A=(2,4),B=(9,12),P=(14,8)$

${}_4=(100),{}_4=1ra\frac{d}{s},a_4=-2ra\frac{d}{s^2}$

Hint: This problem may look like one you completed when we studied instant centers, which could be useful for performing a sanity check on your answers

a$)$ Write out the vector loop equations for the position, velocity, and acceleration of $P$

b$)$ Compute the lengths of $O_{2}A,O_2{O}_4,AB,B{O}_4,$ and AP

c$)$ Compute the angles ${}_2,{}_3,{}_4,{}_5$

d$)$ Compute the angular velocities ${}_2,{}_3,{}_4,{}_5$

e$)$ Compute the angular accelerations $a_2,a_3,a_4,a_5$