The figure above shows two rods OP and PR in the xy-plane. The rods, each 10cm long, are hinged at P. The end O is fixed while the end R can move along the positive x-axis. OL=20cm, OR=s cm and angle POR = θ, where 0 ≦ θ ≦ pi/2.

s = 20 cos θ, I have done this.

I don't know how to solve :

a ) If R moves from the poin O to the point L at a speed of 10cm/s, find the rate of change of θ with respect to time when s = 10.
b ) Find the equation of the locus of the mid-point of PR
c ) A square of side p cm is inscribed in triangle OPR such that one side of the square lies on OR. Show that
　　20 sinθ cosθ
p = ---------------
　　sinθ + 2cosθ
Hence, find θ when the area of the square is a maximum.

Thank you very much!
ps.+個人感受: 微分既文字題真係好難

a)
Let mid-pt of OR be M, then OM = s/2.

(Since triangle OPM and RPM are right-angled triangle, with angle OMP and RMP = 90 degree,)
cosθ = (s/2) / (10)
s = 20 cosθ

ds/dt = ds/dθ ‧ dθ/dt
10 = (ds/dθ do it yourself, I forgot) ‧ dθ/dt
then you can find dθ/dt