Question

A 5g bullet is fired from 800g pistol with speed of 50 m/s. What is the speed of the recoil of the Pistol

Answer 1

Answer

Given -

$\sf{m_b = 5g}$

$\sf{m_g = 800g}$

$\sf{v_b = 50 m/s }$

$\longrightarrow$$m_b$ mass of bullet

$\longrightarrow$$v _b$ velocity of bullet

$\longrightarrow$$m_g$ mass of gun

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To find -

Recoil velocity of gun

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Solution

When bullet is fired from gun then

$\implies$$\sf{P_{initial} = 0}$

$\implies$$\sf{P_{final} = m_b v _b + m_g v_g}$

where

$\longrightarrow$$m_b$ mass of bullet

$\longrightarrow$$v _b$ velocity of bullet

$\longrightarrow$$m_g$ mass of gun

$\longrightarrow$$v_g$ velocity of gun

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By Law of conservation of linear momentum

$\implies$$\sf P_{initial} = P_{final}$

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$\implies$$\sf{P_{final} = m_b v _b + m_g v_g = 0}$

$\boxed{\rm{V_g = \frac{ - m_bv_b}{m_g}}}$

$V_g$ $\longrightarrow$ recoil velocity of gun

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$\longrightarrow$$\sf{m_b = 5g}$

$\longrightarrow$$\sf{m_g = 800g}$

$\longrightarrow$$\sf{v_b = 50 m/s }$

Substituting the values -

$\implies$$\rm{V_g = \frac{ - 5 \times 50}{800} = - 0.3125}$

The gun recoils with the speed of 0.3125 m/s

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Thanks

Answer 2

Given ,

Mass of bullet (m) = 5 g or 0.005 kg

Mass of pistol (M) = 800 g or 0.8 kg

Velocity of bullet (v) = 50 m/s

We know that , the recoil velocity of gun is given by

$\boxed{ \sf{Recoil \: velocity \: (V) = - \frac{mv}{M} }}$

Thus ,

V = -0.005 × 50 / 0.8

V = -0.3125 m/s

Here , the negative sign of V shows the recoil velocity of pistol is opposite to the velocity of bullet

∴ The recoil velocity of pistol is 0.3125 m/s