Answer
$\approx$ $0.396$ $m/min$
Work Step by Step
we are given
$\frac{dθ}{dt}$ = $2°/min$ = $\frac{\pi}{90}$ $rad/min$
$x^{2}$ = $12^{2}+15^{2}-2(12)(15)cosθ$ = $369-360cosθ$
$x^{2}$ = $369-360cosθ$
$2x\frac{dx}{dt}$ = $360sinθ\frac{dθ}{dt}$
$θ$ = $60°$
$x$ = $\sqrt {369-360cos60°}$ = $3\sqrt {21}$
$\frac{dx}{dt}$ = $\frac{180sin60°}{3\sqrt {21}}\frac{\pi}{90}$
$\frac{dx}{dt}$ $\approx$ $0.396$ $m/min$
