The speed at the bottom of the slope is 31.3 m/s
Explanation:
Due to the law of conservation of energy, as the boulder rolls down, its initial gravitational potential energy is converted into kinetic energy. At the bottom of the slope, eventually, all the gravitational potential energy has been converted into kinetic energy, so we can write:
[tex]U_i = K_f \rightarrow mgh = \frac{1}{2}mv^2[/tex]
where:
[tex]U_i=mgh[/tex] is the initial gravitational potential energy, with
m = 100 kg is the mass of the boulder
[tex]g=9.8 m/s^2[/tex] is the acceleration of gravity
h = 50 m is the initial heigth
[tex]K_f = \frac{1}{2}mv^2[/tex] is the final kinetic energy of the boulder, with
v = ? being the final speed of the boulder
And solving for v, we find:
[tex]v=\sqrt{2gh}=\sqrt{2(9.8)(50)}=31.3 m/s[/tex]
Learn more about potential energy and kinetic energy:
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