Object A has a position as a function of time given by r A(t) = (3.00...

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Object A has a position as a function of time given by r A(t) = (3.00...

Object A has a position as a function of time given by r A(t) = (3.00 m/s)t i^ + (1.00 m/s2)t2 j^. Object B has a position as a function of time given by rB(t) = (4.00 m/s)t i^ + (−1.00 m/s2)t2 j^. All quantities are SI units. What is the distance between object A and object B at time t = 3.00 s?

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Answer 1

Answer #1

r A(t) = (3.00 m/s)t i^ + (1.00 m/s²)t2 j^.

rB(t) = (4.00 m/s)t i^ + (−1.00 m/s²)t2 j^.

time t = 3.00 s

r A(t=3) = 9.00 i^ + 9.00 j^.

rB(t=3) = 12 i^ + −9 j^.

r(B,(t=3))-r(A,(t=3))=3i+18j

sqrt(3²+18²)=18.24 is the distance after 3 seconds

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Answer 2

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