Two 20 kg cannon balls are chained together and fired horizontally with a velocity of 200 m//s from the top of a 30 m wall. The chain breaks during the flight of the cannon balls and one of them strikes the ground at t=2s, at a distance of 250 m from the foot fo the wall, and 5 m to the right of line of fire determine the position of the other cannon ball at that instant Neglect the resistance of air.

Two 20 kg cannon balls are chained together and fired horizontally wit

1.	Two 20 kg cannon balls are chained together and fired horizontally with a velocity of 200 m//s from the top of a 30 m wall. The chain breaks during the flight of the cannon balls and one of them strikes the ground at t=2s, at a distance of 250 m from the foot fo the wall, and 5 m to the right of line of fire determine the position of the other cannon ball at that instant Neglect the resistance of air.
Answer» Solution :As no external force acts in `z` direction, HENCE `z` - coordinate of the centre of MASS of he ball should be zero. To make `z`-coordinate zero other ball should fall symmetricaly with respect to `z` axis. Hence `z`-coordinate of other ball `=-5m`. The balls do not have any exeternal force in `X` direction. Hence in `x` direction the centre of mass shouldmove with constant VELOCITY. `x` coordinate of centre of mass at `t=1.5 s=200xx2=400m` Hence `x_(CM)=(m_(1)x_(1)+m_(2)x_(2))/(m_(1)+m_(2))` `400=(20xx250+20x_(2))/(20+20)` ` x_(2)=800-250=550m` Height fallen by centre of mass at `t=2s`, `h=1/2xx10xx(2)^(2)=20m` Hence `y` coordinate of centre of mass `=30-20=10n` Hence `y_(CM)=(m_(1)y_(1)+m_(2)y_(2))/(m_(1)+m_(2))` `10=(20xx0+20xxy_(2))/(20+20)` `implies y_(2)=20m`