Question

From a rifle of mass 4 kg, a bullet of mass 50 g is fired with an initial velocity of 35 m s–1 . Calculate the initial recoil velocity of the rifle

NCERT Class IX
Sciences - Main Course Book

Chapter 9. Force and Laws of Motion

Answer 1

M = 4 kg              m  = 50 gms
v  = 35 m/sec

initial momentum of rifle and bullet together = 0.  So  as per the conservation of linear momentum,
       0 = M * (-V) +  m  v 
=>     0   = 4 * (-V) + 50/1000  * 35
 
V =  0.4375  m/sec    recoil velocity

Answer 2

Answer:

The recoil velocity of the rifle is 0.44 m/sec  

Explanation:

Given mass of a rifle, $m_{1} = 4 kg$

          mass of bullet $m_{2} = 50 g=0.05kg$

          velocity of the bullet,  $v_{2} = 35 m/s$

Applying principle of conservation of linear momentum,

       $m_{1} u_{1} +m_{2} u_{2} =m_{1} v_{1} +m_{2} v_{2}$

Since, initially rifle and bullet are together in a system, $LHS=0$ Therefore

                   $m_{1} v_{1} +m_{2} v_{2}=0$

    $\implies 4\times v_{1} +0.05\times 35=0$

                             $\implies v_{1}= \frac{-0.05\times 35}{4} \approx-0.44m/s$

Hence, the recoil velocity is 0.44 m/sec  

Negative sign shows that the recoil velocity is opposite to the direction of motion of the object.