Answer:
[tex]v=33.42 \frac{m}{5}[/tex]
Explanation:
Hello
The principle of conservation of energy indicates that energy is not created or destroyed; It only is transformed in some ways into others. In these transformations, the total energy remains constant; that is, the total energy is the same before and after each transformation.in this case the potential energy is the mechanical energy associated with the location(heigth) Ec=mgh, here m is the mass, g is the acceleration due to gravity and h is the height
[tex]E_{g}=mgh[/tex]
and , it must be equal to the kinetic energy in the bottom, it is given by
[tex]E_{k}=\frac{mv^{2}}{2}\\[/tex]
where m is the mass of the object , and v its velocity
According to the principle of conservation of energy
[tex]E_{g}=E_{k}\\mgh=\frac{mv^{2} }{2} \\Now, isolate\ v\\gh=\frac{v^{2} }{2} \\2gh=v^{2}\\\sqrt{2gh} =v\\[/tex]
the velocity only can be positive, it means we need just the positive root
Replacing
[tex]v= \sqrt{2gh} \\v= \sqrt{2(9.8 \frac{m}{s^{2} } )*57m} \\v=\sqrt{\frac{117.2m^{2} }{s^{2} } } \\v=33.42 \frac{m}{5}[/tex]
Have a great day
