Answer:
-0.4 m/s
Explanation:
We can solve this problem by using the law of conservation of momentum. In fact, the total momentum of the shell + cannon system must be conserved.
Before the shot, the total momentum of the system is zero:
p = 0
After the shot, the total momentum is:
[tex]p=mv +MV[/tex]
where
m = 3.0 kg is the mass of the shell
v = 200 m/s is the velocity of the shell
M = 1500 kg is the mass of the cannon
V is the recoil velocity of the cannon
Since momentum is conserved, the initial and final momenta must be equal, therefore:
[tex]0=mv+MV\\V=-\frac{mv}{M}=-\frac{(3.0)(200)}{1500}=-0.4 m/s[/tex]
Where the negative sign indicates that the cannon moves in the opposite direction to the shell.
