Question

A revolutionary war era cannon is used in a demonstration. If the 200 kg cannon is on wheels when it's fired, it recoils. if the recoil speed is 0.8 m/s, what is the speed of the 9 kg cannon ball?

Answer 1

The speed of the cannonball can be determined using the principle of conservation of momentum.

Step-by-step explanation:

The speed of the cannonball can be determined using the principle of conservation of momentum. According to this principle, the total momentum before the firing of the cannon is equal to the total momentum after the firing. The recoil speed of the cannon is given as 0.8 m/s.

Let's denote the mass of the cannonball as m1 and its speed as v1, and the mass of the cannon as m2 and its speed as v2. Since both the cannonball and the cannon are initially at rest, we can write:

Total momentum before firing = (mass of cannonball) * (initial speed of cannonball) + (mass of cannon) * (initial speed of cannon) = 0

Total momentum after firing = (mass of cannonball) * (final speed of cannonball) + (mass of cannon) * (recoil speed of cannon)

Using the given information, we can solve for the final speed of the cannonball:

0 = 9 kg * v1 + 200 kg * 0.8 m/s

Solving this equation, we find that the final speed of the cannonball (v1) is approximately -0.071 m/s.

Answer 2

17.8 m/s

Step-by-step explanation:

This is a conservation of momentum problem.

Momentum = p = mv

x = speed of the cannon ball

(200 kg)(0.8 m/s) = (9 kg)(x)

x = (160 kg·m/s) / (9 kg) = 17.8 m/s