Question

Johnny and Francis are participating in the Roller Skating dance championship. While 73.0-kg Johnny roller skates backwards at 3.0 m/s, 57.0-kg Francis jumps into his arms with a velocity of 5.0 m/s in the same direction. How fast do they roll backwards together?

Answer 1

Given,

The mass of Johnny, m₁=73.0 kg

The mass of Francis, m₂=57.0 kg

The initial velocity of Johnny, u₁=3.0 m/s

The initial velocity of Francis, u₂=5.0 m/s

From the law of conservation of momentum, the total momentum of a system will always remain the same.

Therefore,

`m_1u_1+m_2u_2=(m_1+m_2)v`

Where v is the velocity with which they roll backward together.

On substituting the known values in the above equation,

`\begin{gathered} 73.0*3.0+57.0+5.0=(73.0+57.0)v \\ v=(219+285)/(130) \\ =3.88\text{ m/s} \end{gathered}`

Thus the velocity with which they roll backward together is 3.88 m/s