An object initialy at rest explodes and splits into three fragments. The first f

Question

An object initialy 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. The third fragment will fly off toward a general direction of (1) southwest, (2)north of east, or (3) either due north or due east. Why? (b) If the object has a mass of 3.0 kg, the first fragment has a mass of 0.50 kg and a speed of 2.8m/s, and the second fragment has a mass of 1.3 kg and a speed of 1.5m/s, what are the speed and direction of the third fragment?

Explanation / Answer

a) answer is (2) because the vector sum of the three momentum mustbe zero due to momentum conservation. b) m1*v1 = 0.50*2.8 = 1.4 kgm/s, direction: to the west m2*v2 = 1.3*1.5 = 1.95 kg-m/s, direction: to the south m3*v3 = (3.0 - 0.50 - 1.3)*v3 = 1.2*v3 in the east direction: 0 = -1.4 + 1.2*v3x, sov3x = 1.4/1.2 = 1.167 m/s in the north direction: 0 = -1.95 + 1.2*v3y, sov3y = 1.95/1.2 = 1.625 m/s so v3 = 2.0 m/s, direction: arctan(1.625/1.167) = 54onorth of east

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