## Physics (10th Edition)

$\overline P=1.69\times10^4W$
According to the work-energy theorem, $$W=\frac{1}{2}m(v_f^2-v_0^2)$$ We have $m=184kg, v_0=0,$ and $v_f=26m/s$, so the amount of work which must be done by the winch is $$W=62192J$$ To find the power the winch must supply, we also need to find the amount of time to accelerate the glider, which can be found with the equations of kinematics: $$s=\Big(\frac{v+v_0}{2}\Big)t$$ $$t=\frac{2s}{v+v_0}=\frac{2\times48}{26}=3.69s$$ So, $$\overline P=\frac{W}{t}=1.69\times10^4W$$