An object A is dropped from rest the top of a 30 m 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 mximum height above the ground level attained by the centre of mass of the A and B system (take g = 10 m//s^(2))

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

1.	An object A is dropped from rest the top of a 30 m 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 mximum height above the ground level attained by the centre of mass of the A and B system (take g = 10 m//s^(2))
Answer» SOLUTION :`m_(1)=4kg, m_(2)=2kg` Initially 4 KG is on the ground `therefore x_(1)=0` 2 kg is on top of the building `therefore x_(2)=30m` `X_(cm)=(m_(1)x_(1)+m_(2)x_(2))/(m_(1)+m_(2))` `=(0+2xx30)/(4+2)=10m` `therefore` Initial height of CM = 10 m. Initial velocity of CM, `u_(cm)=(m_(1)u_(1)+m_(2)u_(2))/(m_(1)+m_(2))` `u_(cm)=(4xx15+0)/(4+2)=10` m/s UPWARDS `therefore` Maximum height attained by CM from initial position, `h_(cm)=(u_(cm)^(2))/(2g)=(10^(2))/(20)=5m` `therefore` Maximum height attained by CM of 4 kg and 2 kg from the ground `= 10+5=15 m`