A projectile of mass 5 kg, in its course of motion explodes on its own into two fragments. One fragment of mass 3 kg falls at three fourth of the range R of the projectile. Where will the other fragment fall? .

Explanation

It is an explosion of its own without any external influence. After the explosion, the center of mass of the projectile will continue to complete the parabolic path even though the fragments are not following the same parabolic path. After the fragments have fallen on the ground, the center of mass rests at a distance R (the range) from the point of projection as shown in the diagram.
It is an explosion of its own without any external influence. After the explosion, the center of mass of the projectile will continue to complete the parabolic path even though the fragments are not following the same parabolic path. After the fragments have fallen on the ground, the center of mass rests at a distance R (the range) from the point of projection as shown in the diagram.

`m_(1)x_(1)=m_(2)x_(2)`
where `m_(1)=3 kg, m_(2)=2kg x_(1), (1)/(4) R`. the value of `x_(2)=d`
`3xx(1)/(4)=2xxd,`
`d=(3)/(8)R`
The distance between the point of launching and the position of 2 kg mass is `R+d`
`R+d=R+(3)/(8)R=(11)/(8)R=1.375R`
he other fragment falls at a distance of 1.375R from the point of launching. (Here range of the projectile.)