Question

A man of mass $m_1$ is standing on a platform of mass $m_2$ kept on a smooth horizontal surface. The man starts moving on the platform with a velocity $v_r$ relative to the platform. Find the recoil velocity of platform.

Answer 1

Suppose the man moves at a speed u towards right and the platform recoils at a speed v towards left,

both relative to the smooth surface.

Thus, the speed of man relative to the platform is u + v.

u + v = $V_r$

or v = $V_r-u$ . . . . ( 1 )

Taking the platform and be man to be the system, there is no external horizontal force on the system.

The linear momentum of the system remains constant.

Initially both the man and the platform were at rest.

so, 0 = $m_{2}v-m_{1}u$

or $m_{2}v=m_1(V_r-v)$

v = $\frac{m_1{V}_r}{m_1+m_2}$