An object A is dropped from rest the top of a 30m high building and at the same moment another object B is projected vertically upwards with an initial speed of 15 m/s from the base of the building. Mass of the object A is 2 kg while mass of the object B is 4 kg. Find the maximum height above the ground level attained by the centre of mass of the A and B system (take g=10m//s^(2) )

An object A is dropped from rest the top of a 30m high building and at

1.	An object A is dropped from rest the top of a 30m high building and at the same moment another object B is projected vertically upwards with an initial speed of 15 m/s from the base of the building. Mass of the object A is 2 kg while mass of the object B is 4 kg. Find the maximum height above the ground level attained by the centre of mass of the A and B system (take g=10m//s^(2) )
Answer» Solution : `m_(1)=4kg, m_(2)=2KG` Initially 4 kg is on the ground `:.x_(1)=0` 2 kg is on top of the building `:.x_(2)=30m` `x_(CM)=(m_(1)x_(1)+m_(2)x_(2))/(m_(1)+m_(2))` `=(0+2xx30)/(4+2)=10m` `:.` Initial height of CM =10m. Initial velocity of CM, `u_(cm)=(m_(1)u_(1)+m_(2)u_(2))/(m_(1)+m_(2))` `u_(cm)=(4xx15+0)/(4+2)=10m//s` upward. Acceleration of CM, `a_(cm)=g=10m//s^(2)` DOWNWARDS `:.` Maximum height attained by CM from initial position, `h_(cm)=(u_(cm)^(2))/(2g)=(10^(2))/(20)=5m` `:.`Maximum height attained by CM of 4 kg and 2 kg from the ground = 10 + 5 = 15 m