Question

From a rifle of mass 6 kg, a bullet of mass 100 g is fired with an initial velocity of 25 m s. Calculate the initial recoil velocity of the rifle

Answer 1

Given :

➳ Mass of rifle = 6kg

➳ Mass of bullet = 100g = 0.1kg

➳ Velocity of bullet = 25m/s

To Find :

⟶ Recoil velocity of rifle.

Concept :

➠ Since, no external force acts on the system (bullet + rifle), we can easily apply concept of momentum conservation to solve this question.

➠ Momentum is defined as the product of mass and velocity.

➠ Initial momentum of system = zero (i.e., rest)

Calculation :

$\longrightarrow\tt\:P_{initial}=P_{final}$

$\longrightarrow\tt\:0=P_{Rifle}+P_{Bullet}$

$\longrightarrow\tt\:0=MV+mv$

$\longrightarrow\tt\:V=-\dfrac{mv}{M}$

$\longrightarrow\tt\:V=-\dfrac{0.1\times25}{6}$

$\longrightarrow\underline{\boxed{\bf{V=-0.42\:ms^{-1}}}}$

[Note : -ve sign shows opposite direction]

Answer 2

EXPLANATION.

• GIVEN

mass of bullet M1 = 100 g = 0.1 kg

mass of riffle M2 = 6kg

velocity of bullet V1 = 25 m/s

recoil velocity of the riffle = V2

Total mass = M1 + M2

6 + 0.1 = 6.1 kg

since the system was at rest

velocity v = 0

momentum = mass X velocity

( m1 + m2) v

6.1 X 0

0 kg m/s

momentum =

momentum of bullet + momentum of riffle

M1v1 + M2V2

0.1 X 25 + 6 X v2

5/2 + 6v2

since total momentum remain constant

Total momentum before firing = total momentum

of after firing

0 = 5/2 + 6v2

v2 = -5/12

v2 = -0.416 m/s

Therefore,

recoil velocity of pistol = -0.416 m/s

note = also see the image attachment.