Question

Related Time Rates Problem.
AB & AC are two interacting roads enclosing an angle of measure 60 degrees. A bicycle moved on the road AB starting from A with uniform velocity of 16 Km/hr. 15 minutes later another bicycle moved on the road AC starting form A with uniform velocity 20 Km/hr. Find the rate of change of the distance between the two bicycles 15 minutes after starting of the second bicycle.

Answer 1

the derivative of the pythag thrm should be useful

Answer 2

or maybe not :)

Answer 3

law of cosines is a generalization pythag thrm and could be useful

Answer 4

a^2 = b^2+c^2-2bc cos(A)

2a a' = 2b b' + 2c c' - 2b'c cos(A) -2bc' cos(A)

a a' = b b' + c c' - b'c cos(A) - bc' cos(A)

a' = (b b' + c c' - b'c cos(A) - bc' cos(A)) / a


a' = (30(16)(16) + 15(20)(20) - (16)15(20) cos(30) - 30(16)(20) cos(30))
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/(distance between the bikes)

Answer 5

and distance between the bikes is just the solution of the law of cosines

a^2 = b^2+c^2-2bc cos(A)

a = sqrt(b^2+c^2-2bc cos(A))

a = sqrt(30^2 16^2 + 15^2 20^2 - 2(30)(15)(15)(20) cos(30))

Answer 6

Thanks for your help. I appreciate it. :)