A body of mass 1 kg at rest explodes into three fragments of masses in the ratio 1 : 1 : 3 . The two pieces of equal mass fly in mutually perpendicular directions with a speed of `30 m//s` each . What is the velocity of the heavier fragment ?

Explanation

As total mass is 1 kg and fragments masses are in the ratio 1 : 1 : 3 , therefore ,
` m_(1) = m_(2) = (1)/(5) kg and m_(3) = (3)/(5) kg `
also, ` upsilon_(1) = upsilon_(2) = 30 m//s , upsilon_(3) = ` ?
According to the principal of conservation of linear momentum
` vec(p_(1))+ vec(p_(2))+ vec(p_(3))=0 `
` vec(p_(3))+ vec(p_(1))+ vec(p_(2))=sqrt(p_(1)^(2)+p_(2)^(2))`
` m_(3) upsilon =m_(1) sqrt(upsilon_(2)^(1)+ upsilon_(2)^(2))=(1)/(5)sqrt(30^(2)+30^(2)`
` (3)/(5)upsilon_(3) =6 sqrt2 `
` upsilon_(3) = (6 sqrt2xx5 )/(5)=10 sqrt2 = 14 . 14 m//s ` .