I dont understand how to figure this out. Help!?

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Answer 1 · 2017-08-13T05:41:57

The rate of change of #theta# is #=0.06rads^-1#

We need

#cos^2theta+sin^2theta=1#

#1+tan^2theta=sec^2theta#

#(tantheta)'=sec^2theta#

Here, in the figure

#tantheta=h/6#

#h=6tantheta#

Differentiating with respect to #t#

#(dh)/dt=6sec^2theta(d theta)/dt#

#sec^2theta=1+h^2/36=(36+h^2)/36#

Therefore,

#(dh)/dt=6sec^2theta(d theta)/dt=6*(36+h^2)/36*(d theta)/dt#

#(d theta)/dt=6/(36+h^2)*(dh)/dt#

Here,

#h=8 u#

#(dh)/dt=1us^-1#

So,

#(d theta)/dt=6/(36+h^2)*(dh)/dt=6/(36+64)*1=6/100=0.06rads^-1#