SOLUTION: Two cyclists A and B leave X simultaneously at 120° to each other, with constant speeds of 12m/s and 16m/s respectively. Find the rate at which the distance between them is changin

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Question 1105902: Two cyclists A and B leave X simultaneously at 120° to each other, with constant speeds of 12m/s and 16m/s respectively. Find the rate at which the distance between them is changing after 2 minutes.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Position of A :
(12t,0)
Position of B :
(16cos%28120%29t, 16sin%28120%29t)
(-8t, 8sqrt%283%29t)
Using the distance formula,
D%5E2=%2812t-%28-8t%29%29%5E2%2B%288sqrt%283%29t-0%29%5E2
D%5E2=400t%5E2%2B192t%5E2
D%5E2=592t%5E2
D=4sqrt%2837%29t
So then,
dD%2Fdt=4sqrt%2837%29
Constant for all times.