4 seconds later, the cars are getting closer together at ______________________ m/s. (Enter your answer rounded to 3 decimal places)

Question

Two cars are moving towards an intersection. One car is 180 meters north of the intersection and moving towards the intersection at 15 m/s, while the other is 80 meters west of the intersection and moving away from the intersection at 11 m/s.

Answer 1

180 m getting closer at 15 m/sec

80 m getting further away at 10 m/sec

in 4 seconds they are 180-4(15) = 120 m away

and 80+4(10) = 120 m away

construct a right triangle with 2 sides 120 each

the hypotenuse = 120sqr2

h^2 = w^2 + n^2

take the derivative with respect to time

2hh' = 2ww' + 2nn'

divide by 2h

h' = (ww'+nn')/h

plug in values for w=120, n=120, w'=10, n'=-15, h=120sqr2, and solve for h'=rate of change of distance between the two cars

h' = (120(10) +120(-15))/120sqr2

= -5/sqr2 = -5sqr2/2 = about -2.5(1.414) = about -3.536 meters per second