Answer :
Her kinetic energy as she dives into the pool is 780 J
Explanation:
According to the law of conservation of energy, if there are no frictional forces acting on Haley, her mechanical energy must be conserved during the fall:
[tex]U_i +K_i = U_f + K_f[/tex]
where
[tex]U_i[/tex] is the initial potential energy, at the top
[tex]K_i[/tex] is the initial kinetic energy, at the top
[tex]U_f[/tex] is the final potential energy, at the bottom
[tex]K_f[/tex] is the final kinetic energy, at the bottom
Since the initial kinetic energy is zero and the final potential energy (when she reaches the water) is zero, this means that the final kinetic energy must be equal to the gravitational potential energy when she is still at the top:
[tex]K_f = U_i[/tex]
Therefore, we just need to calculate Haley's potential energy at the top, which is given by
[tex]U=mgh[/tex]
where
m is Haley's mass
g is the acceleration of gravity
h is the height relative to the pool
Here we know that,
[tex]mg=390 N[/tex] is Haley's weight
[tex]h=2 m[/tex] is the heigth
Substituting,
[tex]U=(390)(2)=780 J[/tex]
So, the final kinetic energy as she dives into the pool is also 780 J.
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