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Given that,
Mass of Mr. Brooks = 100 kg
A chair lift up to 800 m to the top of the mountain.
To find,
How fast will he be going when he get back to the bottom of the mountain.
Solution,
Let v is the speed when he get back to the bottom of the mountain. Using the conservation of energy to find it.
[tex]\dfrac{1}{2}mv^2=mgh\\\\v=\sqrt{2gh} \\\\v=\sqrt{2\times 9.8\times 800} \\\\v=125.21\ m/s[/tex]
So, the required speed is 125.21 m/s.