Question

Please help me out. :)

Two cars due East at the rate of 90 km/hr and the other due to South at the rate of 60 km/hr, are traveling toward the intersection of two roads. At what rate the two cars approaching each other at the instant when first car is 0.2 km and the second car is 0.15 km from the intersection?

Answer 1

if the eastbound car is at position x(t) and the southbound car is at y(t), the instantaneous distance between them is given by

distance^2 =s^2= x(t)^2+y(t)^2

so that the time rate of change of the distance^2 is

2s ds/dt = 2x dx/dt + 2y dy/dt

dx/dt = - 90 and dy/dt =-60, and we are asked to find the value of ds/dt when (x,y)=(0.2,0.15)

the value of s when (x,y)=(0.2,0.15) is

s=sqrt[0.2^2+0.15^2] =0.25, so we have

2s ds/dt = 2x dx/dt + 2y dy/dt

ds/dt = 1/s(xdx/dt + ydy/dt)
ds/dt=4(-0.2(90)-0.15(60))
ds/dt=-108 km/hr

Answer 2

that's the answer? :)

Answer 3

yes

Answer 4

ahhh, :) THANK YOU VERY MUCH. ^____^