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[AnandDNA]

Two engines, Thomas and Henry, move on close parallel tracks. They strart at the origin, and are togther again at t=e-1. Thomas's displacement-time equation, in units of metres and miniute, is x=300log(t+1), and henry is x=kt, for some constant k

i've worked out an earlier part of the question which is to show k=300/(e-1) which will help in the part im having trouble with.


c) use calculus to find the maximum distance between henry and thomas during the first e-1 minutes, and the time when it occurs

page 85 q.13 from cambridge 3U yr 12

 

[Drongoski]

Two engines, Thomas and Henry, move on close parallel tracks. They strart at the origin, and are togther again at t=e-1. Thomas's displacement-time equation, in units of metres and miniute, is x=300log(t+1), and henry is x=kt, for some constant k

i've worked out an earlier part of the question which is to show k=300/(e-1) which will help in the part im having trouble with.


c) use calculus to find the maximum distance between henry and thomas during the first e-1 minutes, and the time when it occurs

page 85 q.13 from cambridge 3U yr 12

Separation D(t) = 300/(t+1) - 300t/(e-1)

.: dD/dt = 300/(t+1) - 300/(e-1) = 300(e-2-t)/[(t+1)(e-1)]

= 0 at t = e-2

you find dD^2/d^2t = -300/(t+1)^2 always -ve.

.: max separation occurs at t = e-2; to work out this value just sub in t = e-2 into D(t).

 

[AnandDNA]

thanks for that.