The mass of the cannonball is 10 kg
Explanation:
We can solve this problem by applying the law of conservation of momentum: in absence of external forces, the total momentum of the cannon + ball must be conserved before and after the shot.
Before the shot, the total momentum is zero, since both the cannon and the ball are at rest:
[tex]p_i = 0[/tex]
While the total momentum after the shot is
[tex]p_f = mv+MV[/tex]
where
m is the mass of the ball
v = 200 m/s is the velocity of the ball
M = 1000 kg is the mass of the cannon
V = -2 m/s is the recoil velocity of the cannon (negative since it travels in the opposite direction)
Since the total momentum must be conserved,
[tex]p_i = p_f[/tex]
So we can solve the equation to find the mass of the ball:
[tex]0=mv+MV\\m=-\frac{MV}{v}=-\frac{(1000)(-2)}{200)}=10 kg[/tex]
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