The velocity when person enters the water is = 13.3918 m/s
What is law of conservation of energy ?
According to the law of conservation of energy, energy can neither be created nor be destroyed but it can be transformed from one form to another form. In simple words, the total energy of an isolated system always remains constant.
Solving the problem using conservation principle -
Given the mass of the person is (m) = 180 pounds = 81.72 kg
The height of the cliff is (h) = 30 feet = 9.15 m
At the top of the cliff, the person has only potential energy which is given by -
Potential energy (U) = m*g*h
where g is the acceleration due to gravity (g = [tex]9.8 m/s^{2}[/tex]) .
When the person dives down the cliff, then the potential energy gets transformed to Kinetic energy which is given by -
Kinetic energy (K) = [tex]\frac{1}{2}*m*v^{2}[/tex]
where v is the velocity of person as he enters water.
According to principle of conservation of energy ,
Potential energy (U) = Kinetic energy (K)
⇒ m * g * h = [tex]\frac{1}{2}*m*v^{2}[/tex]
⇒ g * h = [tex]\frac{1}{2}*v^{2}[/tex]
∴ v = √(2gh)
⇒ v = √(2 * 9.8 * 9.15) m/s
∴ v = 13.3918 m/s
Thus the velocity when person enters the water is = 13.3918 m/s
To learn more about principle of conservation of energy, refer -
https://brainly.com/question/2847431
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