# The mass of 1 cubic meter of freshwater at the top of a 100 m hydroelectric dam is 1,000 kg and...

## Question:

The mass of 1 cubic meter of freshwater at the top of a 100 m hydroelectric dam is 1,000 kg and it has a potential energy of 980,000 J. At the bottom of the dam, the speed of the moving water is:

a. 44.3 m/s

b. 98 m/s

c. 1,960 m/s

d. 9,800 m/s

## Kinetic Energy and Potential Energy

Kinetic energy describes the motion of an object; while, potential energy is energy due position or location of the object. Here, we are investigating the potential and kinetic energy of a freshwater.

Given:

• mass of freshwater {eq}m = 1000 \ \text{kg}{/eq}
• height {eq}h = 100 \ \text{m}{/eq}
• Potential energy {eq}PE = 980000 \ \text{J}{/eq}

Required:

• velocity of the moving water {eq}v = ?{/eq}

Using the relationship between potential and kinetic energy, we can solve for the velocity of the moving water.

{eq}KE = PE\\ \frac{1}{2}mv^2 = 980000 \ \text{J}\\ \Rightarrow v = \sqrt{\frac{(2)(980000 \ \text{J})}{1000 \ \text{kg}}} \Rightarrow \boxed{v = 44.3 \ \text{m}/\text{s}} {/eq}

{eq}\boxed{a. \ 44.3 \ \text{m}/\text{s}} {/eq} 