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 10 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= 10 m//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 10 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= 10 m//s^2)
Answer» Solution :`m_(1) = 4 kg, 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) = 30 m` `x_(cm) =(m_(1)x_(1) + m_(2)x_(2))/(m_(1) + m_(2)) =(0 + 2 xx 30)/(4+2) = 10 m` `therefore` 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) =(4 xx 15 + 0)/(4+2) = 10` m/s upward. Acceleration of CM, `a_(cm) = g = 10 m//s^(2)` downwards. `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`