Question

from a rifle of mass 4 kilogram A bullet of mass 50g is fired with an initial velocity of 35 ms calculate the initial recoil velocity of the rifle

Answer 1

Mass of the rifle = 4 kg

Mass of the bullet = 50 grams = 0.05 kg

Velocity of the bullet (u) = 35 m/s

Let the recoil velocity of the rile be v.

Since, before firing, the bullet and the rifle are at rest. Hence, the initial momentum of the system (bullet + rifle) is zero.

Hence, after the firing, the final momentum of the system will also be zero.

Final momentum = 4 × v + 0.05 × 35 = 0

$4v = -1.75$

$v = -\frac{1.75}{4}$

v = -0.4375 m/s

The negative sign shows that the velocity will be in opposite direction.

Answer 2

Answer:

Mass of the rifle (m1) = 4 kg

Mass of the bullet (m2) = 50 g = 0.05 kg

Recoil velocity of the rifle = v1

A bullet is fired with an initial velocity (v2) = 35 m/s

Initially, the rifle is at rest.

Thus, its initial velocity (v) = 0

Total initial momentum of the rifle and bullet system

⇒ (m1+m2) × v = 0

The total momentum of the rifle and bullet system after firing

= m1v1 + m2v2

= (4 × v1 ) + (0.05 × 35)

= 4v1 + 1.75

According to the law of conservation of momentum

Total momentum after the firing = Total momentum before the firing

4v1 + 1.75 = 0

v1= -1.75 / 4

v1 = – 0.4375 m/s

The negative sign indicates that the rifle recoils backwards with a velocity of 0.4375 m/s.