Answer
(a) $\Delta U_G = -245~J$
(b) $mass = 2.55\times 10^5~kg$
Work Step by Step
(a) We can find $\Delta U_G$:
$\Delta U_G = U_{Gf} - U_{G0}$
$\Delta U_G = 0 - mgh$
$\Delta U_G = -(1.0~kg)(9.8~m/s^2)(25~m)$
$\Delta U_G = -245~J$
(b) We can find the required mass of water per second:
$P = \frac{E}{t} = 50~MW$
$\frac{(0.80)(245~J/kg)(mass)}{1.0~s} = 50~MW$
$mass = \frac{50\times 10^6~J}{(0.80)(245~J/kg)}$
$mass = 2.55\times 10^5~kg$
