Question

a 30 kg object is moving through space in the +x direction with a speed of 20 m/s when, due to an internal explosion, it breaks into three parts. A 15kg parrt moves away from the explosion with a speed of 10 m/s in the +y direction, a 6kg part moves in the -x direction with a speed of 5m/s. what is the magnitude of the velocity of the remaining part?

Answer 1

Given,

Total mass of object = 30 kg

Initial velocity = (20 m/s) i

After explosion,

mass of first part = 15 kg

velocity of first part = (10 m/s) j

mass of second part = 6 kg

velocity of second part = (5 m/s) -i = (-5 m/s) i

mass of third part = (30 - 15 - 6) kg = 9 kg

let, the velocity of third part is v .

Applying conservation of momentum,

  P_initial = P_final

or,  

or,  

or,  

or,  

This is the velocity of third mass.

So, magnitude of velocity is

  

or,

or,

or,  

or,

Hence, the third part moves with nearly 72 m/s.

NOTE:

Here, i and j are unit vectors along positive x and positive y direction respectively.

Direction of the third part :

So, third part will move in a direction making -13.4 degree(4_th quadrant) with positive x - axis.

For any doubt please comment.