Man starts walking north at 2 ft/s from a point P. Five minutes later a woman starts walking south at 7 ft/s from a point 500 ft due east of P. At what rate are the people moving apart 15 min after the woman starts walking? (Round your answer to two decimal places.)

Step-by-step explanation:

Let consider that vertical axis has its positive side oriented to the north and positive side of the horizontal axis has its orientation to the east. Besides, both persons walk at constant rate. Then, displacement formulas are:

Man

Woman

The minimum distance between the man and the woman can be calculated by means of the Pythagorean Theorem:

The rate of change of such distance is:

The positions and velocities at are:

The rate of change is:

graph b

step-by-step explanation:

one solution- graph a (clear intercepting point.)

no solution- graph b (they're parallel, there will never be a point of interception.)

infinite solutions- graph c (all points intercept.)

x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

step-by-step explanation:

formula

x = x1 + p/w(x2 - x1)

let the line segment ab with a(x1,y1) and b(x2,y2)

a point(x,y) divide ab in the ratio, 2: 3 the x coordinate can be written as

x = x1 + p/w(x2 - x1)

here p=2 and w = 2+3

therefore,

x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

similarly y coordinate y = y1 + 2/5(y2 - y1)