Respuesta :

The final speed of the rock is 19.8 m/s

Explanation:

We can solve this problem by using the law of conservation of energy: the total mechanical energy of the rock (the sum of potential energy + kinetic energy) must be conserved during the fall. Therefore we can write:

[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

We can rewrite the equation as:

[tex]mgh_i + \frac{1}{2}mu^2 = mgh_f + \frac{1}{2}mv^2[/tex]

where:

m = 5 kg is the mass of the rock

[tex]g=9.8 m/s^2[/tex] is the acceleration of gravity

[tex]h_i = 20 m[/tex] is the initial height  of the rock

u = 0 is the initial speed

[tex]h_f = 0[/tex] since the rock falls to the ground

v is the final speed

And solving for v, we find the final speed:

[tex]v=\sqrt{2gh_i}=\sqrt{2(9.8)(20)}=19.8 m/s[/tex]

Learn more about kinetic energy and potential energy:

brainly.com/question/6536722

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Universidad de Mexico