Answer:
-26 m/s (backward)
Explanation:
We can solve this problem by using the law of conservation of momentum.
In fact, the total momentum momentum of the cannon + ball system must be conserved before and after the explosion.
Before the explosion, they are both at rest, so the total momentum is zero:
p = 0
After the explosion, the total momentum is:
where
M = 1.5 kg is the mass of the cannon
m = 0.52 kg is the mass of the ball
v = +75 m/s is the velocity of the ball
V is the velocity of the cannon
Since the momentum is conserved, we can equate the two expressions:
And solving, we find V:
where the negative sign means the direction is opposite to that of the ball.