SOLUTION: two straight paths,inclined to one another at 60 degrees,interesct at a point o.A boy A is on one path 300m from O while a boy B is on the other path 400m from O.angle AOB=60 degre
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Question 759069: two straight paths,inclined to one another at 60 degrees,interesct at a point o.A boy A is on one path 300m from O while a boy B is on the other path 400m from O.angle AOB=60 degrees.Simultaneously the boys begin to run towards O,A with speed 15 kmh-1 and B with speed 12 kmh-1 What is the shortest distance between the two boys?
I calculated Va-Vb=360.6
I couldn't calculate the shortest distance (l) as I do not know the angle between Ab and Va-Vb,
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
two straight paths,inclined to one another at 60 degrees,interesct at a point o.A boy A is on one path 300m from O while a boy B is on the other path 400m from O.angle AOB=60 degrees.Simultaneously the boys begin to run towards O,A with speed 15 kmh-1 and B with speed 12 kmh-1 What is the shortest distance between the two boys?
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The speed of A = 250 meters/min
Speed of B = 200 m/min
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a & b = distance from O at time t (in minutes)
a = 300 - 250t
b = 400 - 200t
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d = distance between A & B at time t
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Without calculus:
Finding the minimum for d is the same as finding the minimum for d^2
The min is the vertex of the parabola
The vertex is on the LOS, Line of Symmetry t = -b/2a
t = 60/42 = 10/7 seconds
Sub for t as below
==================================
Using the 1st derivative:
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d'(t) =
d'(t) =
@ d'(t) = 0:
t = 10/7 minutes
-----------------
d(10/7) = 151.186 meters
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