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An object initially at rest explodes and splits into three fragments. The first fragment flies off to the west, and the second fragment flies off to the south.if the object has a mass of 3.6kg , the first fragment has a mass of 0.58kg and a speed of 2.5m/s , and the second fragment has a mass of 1.1kg and a speed of 1.5m/s , what is the speed of the third fragment?What is the direction of the third fragment?
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Let East Direction be positive and be denoted by vector i
Let North Direction be positive and be denoted by vector j

Since an internal Force is responsible for explosion,
the Net Momentum of the 3 particles = Initial Momentum = 0
=> (0.58)*(-2.5 i ) + (1.1)*(+1.5 j ) + (3.6-{0.58+1.1})* v = 0
=> - 1.45 i + 1.65 j + 1.92 v = 0
=> v = (1.45/1.92) - (1.65/1.92) j = 0.755208333 i - 0.859375 j

Speed = | v | = root((0.755208333)^2 + (- 0.859375)^2) = 1.44056387 m/s

Direction = Tan inverse ( - 0.859375 / 0.755208333 ) = -48.69138599 Degrees
OR +48.69138599 Degrees anticlockwise from the West Direction
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