FREE BODY DIAGRAM calculus
posted by erica on .
A car is traveling north towards an intersection at 60mph at the same time a truck is headed east toward the same intersection at 45mph. Find the rate of change of the distance between the car and truck when the car is 3 miles south of the intersection and the truck is 4 miles west of the intersection. Is this distance increasing or decreasing at that time?

Place the car on the negative y axis and label the distance to the origin y
Place the truck on the negative x axis and label the distance to the origin x
label the distance between them d
then
d^2 = x^2 + y^2
2d dd/dt = 2x dx/dt + 2y dy/dt
dd/dt =(x dx/dt + y dy/dt)/d
Given: when x = 4 , dx/dt = 45
when y = 3 , dy/dt = 60
d = 5 , (did you notice the 345 rightangled triangle ?)
dd/dt = (4(45) + 3(60)/5 = 72
At that moment the distance between them is decreasing at 72 mph
The distance between them is decreasing, since dd/dt is negative. 
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