Question

Motion of Mass Center in One Dimension
A jeep of mass 2400kg is moving along a straight stretch of road at 80km/h. It is followed by a car of mass 1600 kg moving at 60 km/h.
(a) How fast is the center of mass of the two cars moving?
(b) FInd velocities of both the vehicles in centroidal frame.

Answer 1

Velocity of the mass center `vec(v)_(c ) = (m_("jeep")vec(v)_("jeep") + m_("car")vec(v)_("car"))/(m_("jeep") + m_("car"))`
Assuming direction of motion in the positive x-direction, we have
`vecv_c=(m_(jeep)vecv_(jeep)+m_(car)vecv_(car))/(m_(jeep)+m_(car))" "vecv_c=(2400xx80+1600xx60)/(2400+1600)=(72km)`
(b) Velocity of the jeep in centroidal frame `v_((jeep)//c)=80-72=8km/h` in positive x-direction.
Velocity of the car in centroidal frame `V_(car//c)=60-72=-(12km)/h`
`(12km)/h` negative x-direction direction.