Differentiate this relationship with respect to time:
sec^{2}θ(dθ/dt) = 0.4dx/dt
dθ/dt = 0.4(dx/dt)/sec^{2}θ
Notice that the rate of change of the angle, dθ/dt
is a function of both the car speed, dx/dt and the current angle. In
this case dx/dt = 5 is given, but sec^{2}θ must
be determined.
1 second after the car starts,
x = (1)(5) = 5
x + y = 1.6(5) = 8
sec^{2}θ(AD/4)^{2}
= (<(x + y)^{2} +4^{2})/16
=
5
Substituting sec^{2}θ = 5 into θ^{'}_{t} =
0.4x^{'}_{t}/sec^{2}θ gives
dθ/dt =(0.4)5/5
= 0.4 radians/sec |