The mass of 1 cubic meter of fresh water at the top of a 100 m hydroelectric dam is 1,000 kg and it has a potential energy of 980,000 N.At the bottom of the dam,the speed of the moving water is
A)9,800 m/s.
B)1,960 m/s.
C)44.3 m/s.
D)98 m/s.

Question

Quizplus · Accepted Answer

The potential energy of the water at the top of the dam is converted to kinetic energy as the water falls. Assuming no energy losses, we can equate the potential energy at the top to the kinetic energy at the bottom:

mgh = (1/2)mv^2

where m is the mass of the water (1000 kg for 1 cubic meter), g is the acceleration due to gravity (9.8 m/s^2), h is the height of the dam (100 m), and v is the speed of the water at the bottom.

Simplifying the equation and solving for v, we get:
v = sqrt(2gh)

v = sqrt(2 x 9.8 x 100) = 44.3 m/s

Therefore, the correct answer is choice C.

The Mass of 1 Cubic Meter of Fresh Water at the Top