Answer: the recoil velocity of the gun is indeed 0 m/s. This means the gun doesn't move when the bullet is fired due to the conservation of momentum.
To calculate the recoil velocity of the gun when a bullet is fired, you can use the principle of conservation of momentum. The total momentum before the firing should be equal to the total momentum after the firing. The formula for this is:
m1 * u1 + m2 * u2 = m1 * v1 + m2 * v2
Where:
m1 = mass of the bullet = 0.04 kg (converted from 40 g)
u1 = initial velocity of the bullet = 800 m/s
m2 = mass of the gun = 8 kg
u2 = initial velocity of the gun (which is initially at rest, so u2 = 0 m/s)
v1 = final velocity of the bullet (which is its velocity after being fired)
v2 = final velocity of the gun (what we want to calculate)
Now, plug in these values into the equation:
0.04 kg * 800 m/s + 8 kg * 0 m/s = 0.04 kg * v1 + 8 kg * v2
32 kg·m/s = 0.04 kg * v1 + 8 kg * v2
Now, we need to calculate v1, which is the velocity of the bullet after being fired. To do this, we can use the fact that there is no external horizontal force acting on the system after firing (neglecting air resistance). Therefore, the total momentum before firing should be equal to the total momentum after firing.
m1 * u1 = m1 * v1
0.04 kg * 800 m/s = 0.04 kg * v1
v1 = 800 m/s
Now, substitute this value back into the momentum conservation equation:
32 kg·m/s = 0.04 kg * 800 m/s + 8 kg * v2
32 kg·m/s = 32 kg·m/s + 8 kg * v2
Now, solve for v2:
8 kg * v2 = 32 kg·m/s - 32 kg·m/s
8 kg * v2 = 0 kg·m/s
v2 = 0 m/s
So, the recoil velocity of the gun is indeed 0 m/s. This means the gun doesn't move when the bullet is fired due to the conservation of momentum.
Step-by-step explanation: