A 8.0 kg shell leaves a 2.0 x 103 kg cannon, at a speed of 4.0 x 102 m/s. What is the recoil speed of the cannon?

1.6m/s

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What the answer

Well, let's put our thinking caps on and solve this problem. When the shell is fired, momentum is conserved. The initial momentum of the shell and cannon must be equal to the final momentum, so we can set up an equation.

The initial momentum of the shell is given by the mass of the shell (8.0 kg) times its velocity (4.0 x 102 m/s). So the initial momentum of the shell is 3.2 x 103 kg*m/s.

Now, according to Newton's third law, the cannon and shell experience equal and opposite forces. This means that the change in momentum for the cannon will be equal in magnitude but opposite in sign to the momentum of the shell. So the final momentum of the cannon will be -3.2 x 103 kg*m/s.

The final momentum of the cannon can be calculated using the formula p = mv, where p is the momentum, m is the mass, and v is the velocity. We can rearrange this formula to solve for v, the recoil speed of the cannon.

The mass of the cannon is given as 2.0 x 103 kg. Plugging in the values, we get:

-3.2 x 103 kg*m/s = (2.0 x 103 kg) * v

Solving for v, we find that the recoil speed of the cannon is -1.6 m/s.

But wait, hold your horses, did you notice the negative sign? That means the cannon is actually recoiling in the opposite direction of the shell! So in this case, the recoil speed of the cannon is 1.6 m/s, but in the opposite direction. It's like the cannon saying, "Wait, I'm not going to let you take all the spotlight!" So it joins the party with a little recoil dance of its own.

To find the recoil speed of the cannon, we can make use of the principle of conservation of momentum. According to this principle, the total momentum before an event is equal to the total momentum after the event, as long as there are no external forces acting on the system.

The momentum of an object is given by the product of its mass and velocity. Therefore, we can calculate the momentum of the shell before it is fired:

Momentum of the shell before firing = mass of shell x velocity of shell
= (8.0 kg) x (4.0 x 10^2 m/s)

Next, we need to consider the momentum of the cannon after the firing, which would be equal in magnitude but opposite in direction to the momentum of the shell:

Momentum of the cannon after firing = mass of cannon x velocity of cannon (recoil speed)

Since we're looking for the recoil speed of the cannon, let's denote it as v (m/s). Therefore, the momentum of the cannon can be written as:

Momentum of the cannon after firing = (2.0 x 10^3 kg) x (-v)

Now, using the conservation of momentum principle, we can equate the two momenta:

mass of shell x velocity of shell = mass of cannon x velocity of cannon (recoil speed)

(8.0 kg) x (4.0 x 10^2 m/s) = (2.0 x 10^3 kg) x (-v)

Let's solve for v by rearranging the equation:

v = (8.0 kg x 4.0 x 10^2 m/s) / (2.0 x 10^3 kg)
v = (32.0 x 10^2 kg m/s) / (2.0 x 10^3 kg)
v = 16.0 m/s

Therefore, the recoil speed of the cannon is 16.0 m/s.

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