The recoil velocity of the cannon is -0.83 m/s
Explanation:
We can solve this part by using the law of conservation of momentum: in fact, the total momentum of the cannon+ball system before and after the shot must be equal, in absence of external forces.
Before the shot, the total momentum of the system is zero, since both objects are at rest:
[tex]p=0[/tex] (1)
After the shot, the total momentum is:
[tex]p=mv+MV[/tex] (2)
where :
m = 5 kg is the mass of the ball
v = 50 m/s is the velocity of the ball
M = 300 kg is the mass of the cannon
V is the recoil velocity of the cannon
Since momentum is conserved, the momentum before and after must be conserved, so we can find the recoil velocity of the cannon:
[tex]0=mv+MV\\V=-\frac{mv}{M}=-\frac{(5)(50)}{300}=-0.83 m/s[/tex]
where the negative sign means the cannon is moving in the direction opposite to the ball.
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