Momentum problem (explosion)

Question

A 0.45 kg fire-cracker is at rest when it explodes into four pieces.

 

1: 0.15 kg - 15 m/s due east

2: 0.075 kg - 20 m/s due west

3: 0.05 kg - 30 m/s due north

4: 0.175 kg - ?

 

What is the velocity (including direction) of the fourth piece?

 

 

I need help on how to approach this problem. Thank you 

Answer 1

Set up conservation of linear momentum in the x (east-west) and y (north-south) directions.  You will get 2 equations in the unknowns v_x and v_y of the 4th piece, which you can easily solve, and then get the direction from tan^-1(v_y/v_x).

 

x-direction:

 

0.15(15) - 0.075(20) + 0.175v_x = 0

 

Solve for v_x in m/s.

 

y-direction:

 

0.05(30) + 0.175v_y = 0

 

Solve for v_y in m/s.

 

Direction measured counterclockwise from the +x direction:

 

θ = tan^-1(v_y/v_x)

 

Be careful with the choice of a quadrant for θ.  You should be able to solve the problem now.