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
brainly.com/question/1198647
brainly.com/question/10770261
#LearnwithBrainly