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Two particles are moving along two long straight lines, in the same plane, with the...
Two particles are moving along two long straight lines, in the same plane, with the same speed: 20 cm/s. The angle between the two lines is 60° and their intersection point is O. At a certain moment, the two particles are located at distances 3 m and 4 m from O and are moving towards O. Subsequesntly the shortest distance between them will be:
A) 50 cm
B) 40 √2 cm
C) 50 √2 cm
D) 50 √3 cm
1 Answer | add yours
Two particles are moving along straight lines, in the same plane. Their speed is the same and equal to 20 cm/s. The angle between the two lines is 60 degrees and the intersect at point O.
At a certain moment, the two particles are located at distances 3 m and 4 m from O and are moving towards O.
The displacement D of the particle that is initially at a distance 3 m from O can be divided into two components D*cos 60 is in the same direction as the other particle and D*sin 60 is perpendicular to the direction in which the particle is moving.
The distance between the particles after t seconds is `S = sqrt((150*sqrt3 - 10*sqrt 3*t)^2 + (250 - 10t)^2)`
The minimum distance between them is at t when S' = 0
=> `(20*t-350)/sqrt(t^2-35*t+325) = 0`
=> t = 17.5
At t = 17.5, S = `50*sqrt 3`
S'' = `(375*sqrt(t^2-35*t+325))/(t^4-70*t^3+1875*t^2-22750*t+105625) `
At t = 17.5, S'' is positive
As S' = 0 and S'' is positive at t = 17.5 this is a point of minimum value.
The minimum distance between the two particles as `50*sqrt 3` cm
Posted by justaguide on June 23, 2013 at 3:12 AM (Answer #1)
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