A gun (mass = M ) fires a bullet (mass = m ) with speed Vr relative to the barrel of the gun which is inclined at an angle of 60° with horizontal. The gun is placed over a smooth horizontal surface. Find the recoil speed of the gun.

Question

A gun (mass = M ) fires a bullet (mass = m ) with speed Vr relative to the barrel of the gun which is inclined at an angle of 60° with horizontal. The gun is placed over a smooth horizontal surface. Find the recoil speed of the gun. (A) V=(1/2)(( textitmV) textr/( textitm + textitM)) (B) V=(1/2)(( textitmV) textr/( textitm - textitM)) (C) V=(1/2)(( textitMV) textr/(m + M)) (D) None of the above

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-mvdw43a3h6va.png" /> Using conservation of linear momentum in the horizontal direction. m(V r cos 60°-V)=M V ( textitmVr textcos 60 texto/ textitm + textitM)= textitV V=(1/2) (m Vr/(m+M))

Q. A gun (mass = $M$ ) fires a bullet (mass = $m$ ) with speed $V_{r}$ relative to the barrel of the gun which is inclined at an angle of $6 0^{\circ}$ with horizontal. The gun is placed over a smooth horizontal surface. Find the recoil speed of the gun.

$V = \frac{1}{2} \frac{( mV ) _{r}}{( m + M )}$

$V = \frac{1}{2} \frac{( mV ) _{r}}{( m - M )}$

$V = \frac{1}{2} \frac{( MV ) _{r}}{( m + M )}$

None of the above

Using conservation of linear momentum in the horizontal direction.
$m (V_{r} cos 6 0^{\circ} - V) = M V$
$\frac{mV _{r} cos 60 ^{o}}{m + M} = V$
$V = \frac{1}{2} \frac{m V _{r}}{( m + M )}$

Q. A gun (mass = M ) fires a bullet (mass = m ) with speed Vr​ relative to the barrel of the gun which is inclined at an angle of 60∘ with horizontal. The gun is placed over a smooth horizontal surface. Find the recoil speed of the gun.

V=21​(m+M)(mV)r​​

V=21​(m−M)(mV)r​​

V=21​(m+M)(MV)r​​