A 15 g bullet is fired with a velocity of 200m/s from a 6kg rifle. What is the recoil velocity of the rifle?

Idk

To find the recoil velocity of the rifle, we can use the principle of conservation of momentum. According to this principle, the total momentum before the bullet is fired is equal to the total momentum after the bullet is fired.

The momentum of an object is calculated by multiplying its mass by its velocity:

momentum = mass × velocity

Let's denote the mass of the bullet as m1 and the velocity of the bullet as v1. Similarly, let's denote the mass of the rifle as m2 and the recoil velocity of the rifle as v2.

Before the bullet is fired, the rifle and the bullet are not moving, so the initial momentum is zero:

initial momentum = (mass of rifle + mass of bullet) × 0 = 0

After the bullet is fired, the bullet moves forward with a velocity of 200 m/s, and the rifle moves backward with the recoil velocity v2:

final momentum = (mass of rifle × v2) + (mass of bullet × velocity of bullet)

Since the initial momentum is equal to the final momentum, we can set up the following equation:

0 = (6 kg × v2) + (0.015 kg × 200 m/s)

Simplifying the equation gives us:

0 = 6 kg × v2 + 3 kg m/s

Rearranging the equation gives us:

6 kg × v2 = -3 kg m/s

Now, we can solve for v2:

v2 = -3 kg m/s / 6 kg

v2 = -0.5 m/s

Therefore, the recoil velocity of the rifle is 0.5 m/s in the opposite direction.

To find the recoil velocity of the rifle, we can use the law of conservation of momentum. This law states that the total momentum before an event is equal to the total momentum after the event, as long as no external forces are acting on the system.

In this case, the bullet and the rifle form a closed system. Let's consider the bullet's momentum as it is fired from the rifle. The momentum of an object is given by the product of its mass and velocity. The mass of the bullet is 15 g, which is equal to 0.015 kg, and its velocity is 200 m/s.

The momentum of the bullet can be calculated as follows:

Momentum of the bullet = mass of the bullet × velocity of the bullet
= 0.015 kg × 200 m/s
= 3 kg·m/s

According to the law of conservation of momentum, the total momentum before the bullet is fired is zero because the rifle is initially at rest. Therefore, the total momentum after the bullet is fired should also be zero. Let's assume the recoil velocity of the rifle is V (in m/s).

The momentum of the rifle can be calculated as follows:

Momentum of the rifle = mass of the rifle × velocity of the rifle
= 6 kg × V

Since the total momentum after the bullet is fired is zero, we can write:

0 = 3 kg·m/s + 6 kg × V

To find the recoil velocity (V), we rearrange the equation:

6 kg × V = -3 kg·m/s (Note: the negative sign indicates that the rifle moves in the opposite direction to the bullet)

Finally, we solve for V:

V = -3 kg·m/s / 6 kg
= -0.5 m/s

Therefore, the recoil velocity of the rifle is 0.5 m/s in the opposite direction of the fired bullet.