Question

A car with a gun mounted on it is kept on the horizontal frictionless surface. The total mass of the car, gun and shell is $50kg$. Mass of each shell is $1kg$. If the shell is fired horizontally with relative velocity $100m/sec$ with respect to the gun. What is the recoil speed of car after the second shot in a nearest integer?

• A. v = $2m/sec$
• B. v = $10m/sec$
• C. v = $5m/sec$
• D. v = $1m/sec$

Answer 1

The correct option is A v = $2m/sec$

Assume that the velocity of car after recoil $=-v$ (in opposite direction)

And the velocity of wheel w.r.t. ground $=u$

therefore,

$=u-(-v)=u+v=100$

Apply conservation of momentum

$49(-v)+1\left(u\right)=0$

$-49v+u=0$

$u=49v$

$m{v}_1+m{v}_2=0$

On applying law of conservation of momentum

$P_i=P_f$

We get,

$v=2m/s^{-1}$