1. The problem statement, all variables and given/known data A firework at rest with a mass of 0.90kg explodes into 3 pieces. One piece has a mass of 0.25kg and moves horizontally at 36m/s [N]. Another has a mas of 0.35kg and moves horizontally at 32m/s [S50°W] Find the velocity of the third peice 2. Relevant equations SOH CAH TOA Conservation of Momentum Pythagorean Theorem 3. The attempt at a solution Let N and E be positive I first split up both the x and y components v1y=36m/s v1x=0m/s v2y-32cos50=-20.57m/s v2x=-32sin50=-24.51m/s Now I subtracted the 2 masses from .90kg which gave me a mass of .30kg. Then I used the conservation of momentum for both the x and y components, which must equal zero as the object was at rest initially PT=0 0=m1v1fx-m2v2fx+m3v3fx 0=(0.25kg)(0m/s)-(0.35kg)(24.51m/s)+(0.30kg)v3fx v3fx=28.59m/s 0=m1v1fy-m2v2fy+m3v3fy 0=(0.25)(36m/s)-(0.35)(20.57m/s)+(0.30kg)v3fy v3fy=6.0m/s To find the final velocity with the x and y components a2+b2=c2 62+28.592=820 √820=28.63 v3f=28.63m/s Now we find the angle of the magnitude tan-1=(6/28.59) =11.85° However, this is where I'm stuck. How do I know if it is north or south or west or east? I looked at the book and my calculations are correct, but they say it is S11.9W. How do I determine this?