Two cars are moving towards an intersection.

Question

Two cars are moving towards an intersection. One car is moving 170 m north of the intersection and moving towards the intersection at 10 M/S, while the other is 150 m west of the intersection and moving towards the intersection at 15 M/S. How rapidly are the cars approaching each other 2 seconds later?

please help. And show work/ explain how you got to the answer

Answer 1

170 north moving closer at 10 m/sec

150 west moving closer at 15 m/sec

after 2 seconds

they are 170-2(10) = 150 north

and 150-2(15) = 120 west

construct a right triangle with altitude 150 and base 120, the hypotenuse, the distance between them, = h = sqr(150^2+120^2) = 250 meters

h^2 = a^2 + b^2

take the derivative,

this is a related rates problem, a subtopic,

found in textbooks under the topic "derivatives"

2hh' = 2aa' +2bb'

divide by 2h

h'= (aa'+bb')/h

plug in the values, a=150, a'=-10, b=120, b'=-15, h=250, solve for h'

h' = (-1500-1800)/250

= -3300/250 = -330/25

h' = -13.2 m/sec

= rate of change of distance between the two cars after 2 seconds