Hope it will help u !!

Calculation of the Initial Recoil Velocity of the Rifle

To calculate the initial recoil velocity of the rifle, we can use the law of conservation of momentum. According to this law, the total momentum before an event is equal to the total momentum after the event, provided no external forces act on the system.

The momentum of an object is given by the product of its mass and velocity. Therefore, we can use the formula:

Momentum = mass × velocity

Given:
Mass of the rifle (m1) = 4 kg
Mass of the bullet (m2) = 50 g = 0.05 kg
Initial velocity of the bullet (v2) = 35 m/s

Step 1: Converting units
The mass of the bullet is given in grams, but we need to convert it to kilograms to maintain consistency. Therefore, the mass of the bullet is 0.05 kg.

Step 2: Calculating the momentum of the bullet
Momentum of the bullet (p2) = m2 × v2
= 0.05 kg × 35 m/s
= 1.75 kg·m/s

Step 3: Applying the law of conservation of momentum
According to the law of conservation of momentum, the total momentum before the event (bullet fired) is equal to the total momentum after the event (recoil of the rifle).

Initial momentum of the system (before firing) = Final momentum of the system (after firing)

Let the initial velocity of the rifle be v1.

Initial momentum of the system (before firing) = (m1 + m2) × v1

Final momentum of the system (after firing) = (m1 × v1) + (m2 × v2)

Therefore, (m1 + m2) × v1 = (m1 × v1) + (m2 × v2)

Step 4: Solving for the initial recoil velocity of the rifle
Rearranging the equation, we get:

(m1 + m2) × v1 = (m1 × v1) + (m2 × v2)

Expanding the equation, we have:

m1 × v1 + m2 × v1 = m1 × v1 + m2 × v2

Subtracting (m1 × v1) from both sides, we get:

m2 × v1 = m2 × v2

Dividing both sides by m2, we have:

v1 = v2

Therefore, the initial recoil velocity of the rifle is equal to the initial velocity of the bullet, which is 35 m/s.