Question

A 60g bullet fired from a 5kg gun leaves with a speed of 509m/s. find the speed with which the gun recoils​

Answer 1

$\rm{ \pink{\bigstar Fine \longrightarrow }}$

• speed with which the gun recoils

$\rm{ \orange{\bigstar Given \longrightarrow }}$

• Mass of bullet = 60g =60/1000 = 0.06kg
• Speed of the bullet = 509m/s
• Mass of the gun= 5kg

$\rm{ \red{\bigstar Formula \ used \longrightarrow }}$

$\boxed{\sf{MV=mv}}$

where,

M=Mass of bullet

V=velocity of bullet

m= mass of the gun

v=recoil of gun

$\rm{ \blue{\bigstar SoLution \longrightarrow }}$

According to the law of conservation of momentum

Momentum of bullet =momentum of gun

MV=mv

put the given value in the formula we get,

$\sf{\implies 0.06 \times 509 = 5 \times v}$

$\sf{\implies v= \dfrac{0.06\times 509}{5}}$

$\sf{\implies v= 6.108}$

$\small{\bf{\underline{ \therefore \ Recoil \ of \ gun \ is \ 6.1m/s }}}$

________________________

Answer 2

Given :-

• Mass of bullet = 60g = 60/1000 = 0.06kg
• Speed of the bullet = 509 m/s
• Mass of the gun= 5kg

To Find :-

• The speed with which the gun recoils

Formula :-

We know that,

$\blue{\boxed{\sf{MV=mv}}}$

Where,

• M = Mass of bullet
• V = Velocity of bullet
• m = Mass of the gun
• v = Recoil of gun

Solution :-

We have,

$\blue{\boxed{\sf MV = mv}}$

Put the given values in the formula we get,

$\red{\sf{\implies 0.06 \times 509 = 5 \times v}} \\ \\ \blue{\sf{\implies v= \dfrac{0.06\times 509}{5}}} \\ \\ </p><p>\orange{\sf{\implies\boxed{ \sf v= 6.108}}}$

$\green{\large{\sf{{ \therefore \underline{\ Recoil \ of \ gun \ is \ 6.1 \: m/s }}}}}$