A body of mass 1 kg initially at rest explodes and breaks into three fragments of masses in the ration 1 : 1 : 3. The two pieces of equal mass fly off perpendicular to each other with a speed of 30 m/s each. What is the velocity of the heavier fragment?

Explanation

Let the 1 kg mass breaks into three fragments with masses `m_(1), m_(2) and m_(3)` and their velocities are `v_(1), v_(2) and v_(3)` respectively,
Here, `m_(1) + m_(2) + m_(3) = 1` kg
As` m_(1) : m_(2) : m_(3 ) =` 1 : 1 : 3
`therefore " " m_(1) = m_(2) = 0.2 kg , m_(3) = 0.6 kg, v_(1) = v_(2) = 30` m/s
Applying the law of conservation of linear momentum along horizontal direction,
`m_(3)v_(3) = m_(1)v_(1) cos 45^(@) + m_(2) v_(2) cos 45^(@)`
or, `" " 0.6 v_(3) = 0.2 xx 30 xx (1)/(sqrt(2)) + 0.2 xx 30 xx (1)/(sqrt(2)) `
or, `" " v_(3) = (2 xx 0.2 xx 30)/(0.6) xx (1)/(sqrt(2)) = (20)/(sqrt(2))`m/s = 14.14 m/s