March 28, 2017

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A 5.0 kg shell is fired vertically upward. At its max height of 350.0 m, it explodes into 3
pieces. A 1.0 kg chunk lands 15.0 m away, 45
due northeast from the launch site. A second 1.0
kg piece lands 25.0 m, 60
south of east from the launch site. If all 3 pieces land at the same time
on the (level) ground, where does the third piece land?

  • Physics - ,

    Since the shell was at the highest point, its velocity=0. The chunks moved in horizontal plane. Actually, each velocity is horizontal velocity, therefore, these are the velocities of uniform motions.
    v1•t=s1=15, v2•t=s2=25 => v1=0.6•v2,
    p1=m1•v1 =m1•0.6•v2,
    Taking into account the directions of the chunks motions, let’s find the vecor sum of p1 and p2. The angle that p1 and p2 make is 45+60=105º, => (360 - 2•105) =75º. Using the cosine law,
    p12= sqrt{p1²+p2²-2p1•p2•cosα} =
    =sqrt{ {(m1•0.6•v2)² +(m2•v2)² -2m1•m2•v2•0.6•v2•cos75º}.
    p12= m2•v2•sqrt{0.6²+1 - 2•0.6•0.26} =1.02•m2•v2
    According to the law of conservation of linear momentum
    p3 = p12
    p3=m3•v3 =>
    m3•v3 =1.02•m2•v2,
    since m2=1 kg, m3=5-1-1=3 kg,
    v3= =1.02•1•v2/3=1.02•25/3•t.
    s3=v3•t= 1.02•25•t/3•t=1.02•25/3=8.5 m

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