Question 3. Two particles, each of mass m, move in a plane so that their position vectors at time t are given by 2 – t3 – t ri = +(3t – 4)j 1+ t2 (1 – t)(3t² +t+ 2) - T2 = (t – 1)į + 1+t2 (a) Determine the centre of mass of the two particles as a function of t. (b) Show that the path taken by the centre of mass of the two particles lies on a circle. Give the Cartesian equation for that circle. [Hint: after you find the formula for the centre of mass, sketch a few points and then guess the equation of the circle. Then verify that the centre of mass satisfies that equation.]
Question 3. Two particles, each of mass m, move in a plane so that their position vectors at time t are given by 2 – t3 – t ri = +(3t – 4)j 1+ t2 (1 – t)(3t² +t+ 2) - T2 = (t – 1)į + 1+t2 (a) Determine the centre of mass of the two particles as a function of t. (b) Show that the path taken by the centre of mass of the two particles lies on a circle. Give the Cartesian equation for that circle. [Hint: after you find the formula for the centre of mass, sketch a few points and then guess the equation of the circle. Then verify that the centre of mass satisfies that equation.]
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![Question 3. Two particles, each of mass m, move in a plane so that their position vectors at time t
are given by
2 – t3 – t
ri =
+(3t – 4)j
1+ t2
(1 – t)(3t² +t+ 2)
-
T2 = (t – 1)į +
1+t2
(a) Determine the centre of mass of the two particles as a function of t.
(b) Show that the path taken by the centre of mass of the two particles lies on a circle. Give the
Cartesian equation for that circle.
[Hint: after you find the formula for the centre of mass, sketch a few points and then guess the
equation of the circle. Then verify that the centre of mass satisfies that equation.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F948b54fe-206d-4829-84ed-b352ff04bef0%2F8832ea92-400e-4707-a148-d7efb7e64569%2Fod0ot0r.png&w=3840&q=75)
Transcribed Image Text:Question 3. Two particles, each of mass m, move in a plane so that their position vectors at time t
are given by
2 – t3 – t
ri =
+(3t – 4)j
1+ t2
(1 – t)(3t² +t+ 2)
-
T2 = (t – 1)į +
1+t2
(a) Determine the centre of mass of the two particles as a function of t.
(b) Show that the path taken by the centre of mass of the two particles lies on a circle. Give the
Cartesian equation for that circle.
[Hint: after you find the formula for the centre of mass, sketch a few points and then guess the
equation of the circle. Then verify that the centre of mass satisfies that equation.]
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