The additional kinetic energy that the child gains after reaching the bottom of the hill is 200 Joule. The result is obtained by using the principle of Conservation of Mechanical Energy.
The principle of conservation of energy states that "The total energy is neither increased nor decreased in any process. Energy can be transformed from one form to another, and transferred from one object to another, but the total amount remains constant."
In the same way, the Conservation of Mechanical Energy states that the total mechanical energy of a system is conserved. It can be expressed as
[tex]E_{1} = E_{2}[/tex]
[tex]K_{1} + U_{1} = K_{2} + U_{2}[/tex]
[tex]\frac{1}{2} mv_{1} ^{2} + mgh_{1} = \frac{1}{2} mv_{2} ^{2} + mgh_{2}[/tex]
Where
At one point, a child has:
How much more kinetic energy does the child gain at the bottom of the hill?
At the bottom of the hill, the height of the child is zero, h₂ = 0. So, the potential energy is
[tex]U_{2} = mgh_{2}[/tex]
[tex]U_{2} = mg(0)[/tex]
[tex]U_{2} = 0[/tex]
The kinetic energy at the bottom of the hill is
[tex]K_{1} + U_{1} = K_{2} + U_{2}[/tex]
[tex]500 + 200 = K_{2} + 0[/tex]
[tex]K_{2} = 700 J[/tex]
The kinetic energy added for the remainder of the motion is
[tex]K = K_{2} - K_{1}[/tex]
[tex]K = 700 - 500[/tex]
[tex]K = 200 J[/tex]
Hence, the additional kinetic energy that the child gains after reaching the bottom of the hill is 200 Joule.
Learn more about Conservation of Mechanical Energy here:
brainly.com/question/13682185
#SPJ4
