The initial speed of the ball is 5 m/s
Explanation:
We can solve the problem by using the law of conservation of momentum: in absence of external forces, the total momentum of the skater + ball system must be conserved. So we can write:
[tex]p_i = p_f[/tex]
[tex]mu=(m+M)V[/tex]
where:
m = 5 kg is the mass of the ball
u is the initial velocity of the ball
M = 45 kg is the mass of the ice skater
V = 0.5 m/s is the final velocity of the skater+ball together
Solving for u, we can find the initial velocity of the ball:
[tex]u=\frac{m+M}{m}V=\frac{5+45}{5}(0.5)=5 m/s[/tex]
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