A1.5kg cannon is loaded with a 0.52 kg ball . the cannon is ignited and launches the ball forward with speed of 75m/s. determine the post explosion velocity of the cannon.

-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.

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