An object initially at rest explodes and splits into 3 fragments. the first frag

Question

An object initially at rest explodes and splits into 3 fragments. the first fragment flies off to the west, and the second fragment flies off to the south. the third fragment will fly off toward a general direction of? why? if the object has a mass of 3.3kg, the first fragment has a mass of 0.43kg and a speed of 2.6m/s, and the second fragment has a mass of 1.3kg nad a speed of 1.4m/s, what is the speed of the third fragment? what is the direction of the third fragment?

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Explanation / Answer

taking north as j and east as i

Velocity of first particle = v1 = -2.6i

Velocity of second particle = v2 = -1.4j

taking velocity of third particle as v3

Using conservation of momentum

m1v1 + m2v2 + m3v3 = 0

v3 = -(m1v1 + m2v2)/m3

v3 = .712i + 1.159j

Speed = (.712^2 + 1.159^2)^.5 = 1.36 m/s

Direction = invtan(1.159/.712) = 58.43 degrees from east.

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