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

Question

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 south. The third fragment will fly off toward a general direction of (1) southwest (2) north of east, (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 2.8 m/s, and the second fragment has a mass of 1.3 kg and a speed of 1.5 m/s, what are the speed and direction of the third fragment?

Explanation / Answer

This is a conservation of momentum question: For the first part the answer is the third fragment will go northof east. The reason for this is that the total momentum mustbe 0 so in order to counter the force of the first fragment, thethird fragment will have to go east, and to counter the momentum ofthe second fragment, the third will have to go north. It willgo both directions at once, resulting in north of east. For part 2: We know the momentum of the first and second fragments are M=mV=.5(2.8)=1.4N/s M=mV=1.3(1.5)=1.95N/s Now we also know that all of the westerly momentum will be canceledso the westerly velocity of fragment 3 can be calculated using: M=mV; 1.4=1.2V; V=1.1667m/s; note the mass of the third fragment is3-1.3-.5=1.2 Similarily, the southerly momentum will be likewise completelycanceled 1.95=1.2V; V=1.625m/s Now we combine them Vt=(Vw2+Vs2).5 Vt=(1.16672+1.6252).5 Vt=2.33m/s To find the angle we use arcTan =arcTan(1.1667/1.625)=35.68o North of East So the third fragment is traveling 2.33m/s 35.68o N ofE

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