Question

from a rifle of mass 4 kg a bullet of mass 50 gm fired with an initial velocity of 35m/s . calculate the initial recoil velocity of rifle​

Answer 1

AnSwer :

$\dag\:\underline{\sf Given :}$

• Mass of rifle (m₁ ) = 4 kg
• Mass of bullet (m₂) = 50 g = 0.05 kg
• Initial Velocity of the bullet (u₂) = 35 m/s
• Final Velocity of the rifle (v₁) = 0
• Final Velocity of the bullet (v₂) = 0

$\dag\:\underline{\sf To\:Find :}$

• The initial recoil velocity of rifle = ?

$\dag\:\underline{\sf Solution :}$

• In this question we have to apply Law of conservation of momentum :

$:\implies \sf Initial \: Momentum = Final \: Momentum$

$:\implies \sf m_{1} u_{1} + m_{2}u_{2 } =m_{1} v_{1} + m_{2}v_{2}$

$:\implies \sf 4 \times u_{1} + ( - 0.05) \times35 = 4 \times 0 +0.05 \times 0$

$:\implies \sf 4 \times u_{1} + ( -1.75) = 0 + 0$

$:\implies \sf 4 \times u_{1} -1.75 = 0$

$:\implies \sf 4 \times u_{1} = 1.75$

$:\implies \sf u_{1} = \dfrac{1.75}{4}$

$:\implies \sf u_{1} = 0.4375 \: m/s$

$:\implies \underline{ \boxed{ \frak{ u_{1} \approx 0.44 \: m/s}}}$

Hence,the initial recoil velocity of rifle is 0.4375 m/s.

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

The 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.