Two balls of equal mass are projected upwards simultaneously, one from the ground with initial velocity `50ms^-1` and the other from a `40m` tower with initial velocity of `30ms^-1`. The maximum height attained by their COM will be a) 80 m b) 60 m c) 100 m d) 120 m

Explanation

The initial position of centre of mass is
`y_(ic)=(mxx0+mxx40)/(2m)=20m`
Initial velocity of centre of mass
`u_(cm)=(mxx50+mxx30)/(2m)=40ms^(-1)`
Acceleration of centre of mass `a_(cm)=-g`
Using kinematics equation `v_(cm)^2=u_(cm)^2+2a(cm)H`
Here `H` is the maximum height reach by centre of mass of two balls from initial level.
`:. 0^(2)=40^(2)-2xx10xxH`
`impliesH=1600/20=80m`
Hence maximum height reach by centre of mass from ground level will be
`h_(max)=(h_(cm))_("initial")+H=20+80=100m`