The vector position of a 3.50g particle moving in the xy planevaries in the time

Question

The vector position of a 3.50g particle moving in the xy planevaries in the time according to r1 = (3i + 3j)t +2jt2. At the same time, the vector position of a 5.50gparticle varies as r2 = 3i - 2it2 - 6jt,where t is in seconds and r is in cm. At t = 2.50s, determine a.)the vector position of the center of mass b.)the linear momentum of the system c.) the velocity of the center of mass d.)the acceleration of the center of mass e.) the net force exerted on the two particle system. Please show work The vector position of a 3.50g particle moving in the xy planevaries in the time according to r1 = (3i + 3j)t +2jt2. At the same time, the vector position of a 5.50gparticle varies as r2 = 3i - 2it2 - 6jt,where t is in seconds and r is in cm. At t = 2.50s, determine a.)the vector position of the center of mass b.)the linear momentum of the system c.) the velocity of the center of mass d.)the acceleration of the center of mass e.) the net force exerted on the two particle system. Please show work

Explanation / Answer

m1 = 3.50 g, r1 = 3t i + (3t +2t2) j r1' = 3 i + (3 + 4t) j r1'' = 4 j t = 2.50s, r1 = 7.50 i + 20.0 j, r1' = 3 i +13.0 j, r1'' = 4 j m2 = 5.50 g, r2 = (3 - 2t2) i - 6tj, r2' = -4t i - 6 j, r2'' = -4 i, t = 2.50s, r2 = -9.5 i - 15.0 j, r2' =-10 i - 6 j, r2'' = -4 i, a) rc = (m1r1 +m2r2)/(m1 + m2) =(-2.89 i - 1.39 j) cm b) P = m1r1' + m2r2' =(-44.5 i + 12.5 j) g-cm/s c) rc' = P/(m1 + m2) = (-4.94 i +1.39 j) cm/s d) rc'' = (m1r1'' +m2r2'')/(m1 + m2) =(0.44 i - 0.44 j) cm/s2 e) (m1 + m2) rc'' = (4 i - 4 j)g-cm/s2 = (4 i - 4 j) * 10-5 N

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