To find the recoil velocity of the pistol, 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.
Let's denote the recoil velocity of the pistol as Vp and the velocity of the bullet as Vb.
The mass of the bullet is 20 grams, which is equal to 0.02 kg. The mass of the pistol is 2 kg.
Before the bullet is fired, the initial momentum of the system (bullet + pistol) is zero since both the bullet and the pistol are initially at rest.
After the bullet is fired, the total momentum of the system must still be zero to satisfy the conservation of momentum. The momentum of the bullet is given by its mass multiplied by its velocity, and the momentum of the pistol is given by its mass multiplied by its recoil velocity. Therefore, we have the following equation:
(0.02 kg × 150 m/s) + (2 kg × Vp) = 0
Simplifying the equation, we get:
3 + 2Vp = 0
2Vp = -3
Vp = -1.5 m/s
The negative sign indicates that the recoil velocity of the pistol is in the opposite direction to the bullet's velocity. Therefore, the recoil velocity of the pistol is 1.5 m/s in the opposite direction to the bullet's motion.