A10 g projectile is traveling east at 2.0 m/s when it suddenly explodes into three pieces. a 3.0 g fragment is shot due west at 10 m/s while another 3.0 g fragment travels 40◦ north east at 12 m/s. what are the speed and direction of the third fragment?

Lets take

+ x - East

- x - West

+ y - North

- y  - South

Lets take mass of third part is m

m = 10 - 3 - 3 = 4 g

lets speed in x direction is Vx

Speed in y direction is Vy

Linear momentum conservation in x direction,

10 x 2 = [3 x (-10)] + [3 x 12cos40] + [4 x Vx]

Vx = 5.60 m/s

Linear momentum conservation in y direction,

3 x 12 sin40 = 4 x Vy  

Vy= 5.7851 m/s

The resultant speed

V= 8.055 m/s

Angle made with east direction

θ = 45.9°south of east

the area between the graph and the t axis