Awater feature in a garden recycles water with a pump. water is pumped from a stone basin up through a pipe 1 meter high. at that height, the water flows out through a tap and falls down through the air to the basin below, where the cycle begins again. what is the gravitational potential energy of 2.5 kg of water at the top of the pipe? how fast is the falling water moving by the time it reaches the basin?

First we can find the gravitational potential energy at the top of the pipe. PE = mgh PE = (2.5 kg) (9.80 m/s^2) (1 m) PE = 24.5 J The gravitational potential energy at the top of the pipe is 24.5 J. We can find the speed of the water when it reaches the basin. As the water falls, the potential energy is converted into kinetic energy. The kinetic energy at the bottom is equal to the potential energy at the top. KE = PE (1/2) m v^2 = mgh v^2 = 2gh v = sqrt{ 2gh } v = sqrt{ (2) (9.80 m/s^2) (1 m) } v = 4.43 m/s The speed of the water when it reaches the basin is 4.43 m/s

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