Question

A vessel at rest at the origin of an xy coordinate system explodes into three pieces. Just after the explosion, one piece, of mass m, moves with velocity (-47 m/s) and a second piece, also of mass m, moves with velocity (-47 m/s) . The third piece has mass 3m. Just after the explosion, what are the (a) magnitude and (b) direction (as an angle relative to the +x axis) of the velocity of the third piece?

Answer 1

a) 22.06m/s

b)45°

Step-by-step explanation:

Let 'm' be mass of 1st and 2nd pieces

mass of 3rd piece=3m

`v_(1)`=velocity of 1st piece = -47iˆ m/s

`v_(2)`=velocity of 2nd piece = -47jˆ m/s

`v_(3)`=velocity of 3rd piece=?

By considering conservation of linear momentum, we have

m
`v_(1)` + m
`v_(2)` + 3m
`v_(3)`=0

`v_(1)` +
`v_(2)` + 3
`v_(3)`=0

3
`v_(3)`= - (
`v_(1)` +
`v_(2)` )

`v_(3)` = -
`(1)/(3)` (
`v_(1)` +
`v_(2)` )

Substituting the values of
`v_(1)` and
`v_(2)` in above equation

`v_(3)` = -
`(1)/(3)` (-47iˆ -47jˆ ) => 15.6iˆ + 15.6jˆ

(a)Magnitude of the velocity of the third piece is given by

|
`v_(3)`| =√15.6²+15.6² => 22.06m/s

(b) its direction (as an angle relative to the +x axis) 'θ'

θ=
`tan^(-1) ((15.6)/(15.6) )` =>
`tan^(-1) (1 )` =>45°