Answer:
t = 17658 s = 294.3 min = 4.9 h
Explanation:
The general formula for power is:
[tex]P = \frac{W}{t}[/tex]
where,
P = Power of the Motor = 50 KW = 50000 W
W = Work Done by Motor = Change in P.E of Water = mgh
g = acceleration due to gravity = 9.81 m/s²
m = mass of water = ρV
h = depth of water = 180 m
ρ = density of water = 1000 kg/m³
V = Volume of Water = 500 m³
t = time taken = ?
Therefore,
[tex]P = \frac{mgh}{t}=\frac{\rho Vgh}{t}\\\\t = \frac{\rho Vgh}{P}\\\\t = \frac{(1000\ kg/m^3)(500\ m^3)(9.81\ m/s^2)(180\ m)}{50000\ W}\\\\[/tex]
t = 17658 s = 294.3 min = 4.9 h
