A 10G bullet is short from a 5kg gun with a velocity of 400m/s.What is the speed of recoil of the gun?

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Initial momentum = 0

momentum of bullet = mv
momentum of gun = MV

Using conservation of momentum
mv+MV = 0
therefore
V=-mv/M

The momenta of the bullet and the gun are equal (and opposite in direction) after firing. If Vr is the recoil velocity,

5.0*Vr = 0.01 * 400

Solve for Vr, which will be im m/s.

Note that I had to use the same mass units for bullet and gun.

To find the speed of recoil of the gun, we can use 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.

In this case, the bullet and the gun are the two objects involved in the event, so we can consider them as a system. Initially, the bullet is at rest, so its momentum is zero. The gun has a mass of 5 kg and a velocity of 400 m/s. We can calculate the initial momentum of the gun using the formula:

Initial momentum of the gun = mass of the gun × initial velocity of the gun

Initial momentum of the gun = 5 kg × 400 m/s

Next, we consider the final momentum of the system. After the bullet is fired, it has a mass of 10 grams (or 0.01 kg) and a velocity that we need to find. The gun, after firing, recoils in the opposite direction with a velocity we need to calculate as well. Therefore, we can write the final momentum of the system (bullet + gun) as:

Final momentum of the system = momentum of the bullet + momentum of the gun

Final momentum of the system = (mass of the bullet × velocity of the bullet) + (mass of the gun × velocity of the gun)

Final momentum of the system = (0.01 kg × velocity of the bullet) + (5 kg × velocity of the gun)

Now, according to the principle of conservation of momentum, the initial momentum of the system should be equal to the final momentum of the system:

Initial momentum of the system = Final momentum of the system

(5 kg × 400 m/s) = (0.01 kg × velocity of the bullet) + (5 kg × velocity of the gun)

Simplifying the equation, we have:

2000 kg·m/s = 0.01 kg × velocity of the bullet + 5 kg × velocity of the gun

Now we can rearrange the equation to solve for the velocity of the gun:

5 kg × velocity of the gun = 2000 kg·m/s - 0.01 kg × velocity of the bullet

velocity of the gun = (2000 kg·m/s - 0.01 kg × velocity of the bullet) / 5 kg

To find the value of the velocity of the bullet, we need more information. If you provide the mass of the bullet or any other relevant data, I can help you calculate the speed of the gun's recoil.