The initial speed of the ball is 1.98 m/s
Explanation:
The problem can be solved by using the law of conservation of energy.
In fact, since the total mechanical energy of the system must be conserved, the initial kinetic energy of the ball must be all converted into gravitational potential energy of the ball+pendulum system when the system reaches its maximum height (where the motion of the system stops, so the kinetic energy becomes zero).
Therefore, we can write:
[tex]K_i = U_f\\\frac{1}{2}mv^2 = (m+M)gh[/tex]
where
[tex]K_i[/tex] is the initial kinetic energy
[tex]U_f[/tex] is the final potential energy
m = 100.0 g = 0.1 kg is the mass of the ball
M = 2.0 kg is the mass of the pendulum
[tex]g=9.8 m/s^2[/tex] is the acceleration of gravity
h = 20.0 cm = 0.20 m is the change in height of the system
And solving for v, we find the initial speed of the ball:
[tex]v=\sqrt{2gh}=\sqrt{2(9.8)(0.20)}=1.98 m/s[/tex]
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