Problem:
A rifle with a mass of 4 kg fires a bullet with a mass of 50 g and an initial velocity of 35 m/s. We need to calculate the initial recoil velocity of the rifle.

Solution:
To solve this problem, we can apply the principle of conservation of momentum. According to this principle, the total momentum of an isolated system remains constant before and after a collision.

Let's denote the initial velocity of the rifle as Vr and the final velocity of the rifle and bullet combined as Vf. The mass of the rifle is 4 kg, and the mass of the bullet is 50 g, which is equal to 0.05 kg.

Step 1: Convert the mass of the bullet to kilograms
The mass of the bullet is given as 50 g. To convert it to kilograms, we divide it by 1000.
Mass of the bullet = 50 g / 1000 = 0.05 kg

Step 2: Apply the conservation of momentum
According to the conservation of momentum, the sum of the initial momentum of the system (rifle) and the bullet is equal to the sum of the final momentum of the system. Mathematically, we can represent this as:
(mass of rifle * initial velocity of rifle) + (mass of bullet * initial velocity of bullet) = (mass of rifle + mass of bullet) * final velocity

(4 kg * Vr) + (0.05 kg * 35 m/s) = (4 kg + 0.05 kg) * Vf

Simplifying the equation:
4Vr + 1.75 = 4.05Vf

Step 3: Solve for Vr
We need to isolate Vr in the equation. Rearranging the equation, we get:
Vr = (4.05Vf - 1.75) / 4

Step 4: Calculate Vr
Substituting the values into the equation:
Vr = (4.05 * 35 - 1.75) / 4
Vr = (141.75 - 1.75) / 4
Vr = 140 / 4
Vr = 35 m/s

Answer:
The initial recoil velocity of the rifle is 35 m/s.