A loaded spring gun of mass M fires a bullet of mass m with a velocity v at an angle of elevation `theta`. The gun is initially at rest on a horizontal smooth surface. After firing, the centre of mass of the gun and bullet system

Options

A. Moves with a velocity `(vm)/M` along horizontal
B. Moves with a velocity `(vm)/(M cos theta)` in the vertical direction
C. Moves with a velocity `(m v sin theta)/(M + m)` along vertical direction
D. Moves with velocity `v(M - m)//(M + m)` in horizontal direction

Answer

C

Explanation

Vertical velocity of shot after firing = `V sin theta`
`implies` Along horizontal, external force is zero `implies` centre of mass moves in vertical direction
`implies C_(cm) = ((m V sin theta)/(m + M))`.