Aman starts walking north at 4 ft/s from a point p. five minutes later a woman starts walking south at 5 ft/s from a point 500 ft due east of p. at what rate are the people moving apart 15 minutes after the woman starts walking

Both are moving apart with the rate of 8.99 feet per sec.

Step-by-step explanation:

From the figure attached,

Man is walking north with the speed = 4 ft per second

feet per sec.

Woman starts walking due south with the speed = 5ft per second

ft per sec.

We have to find the rate of change in distance z.

From the right angle triangle given in the figure,

We take the derivative of the given equation with respect to t,

-----(1)

Since distance = speed × time

Distance covered by woman in 15 minutes or 900 seconds = 5(900) = 450 ft

y = 4500 ft

As the man has taken 5 minutes more, so distance covered by man in 20 minutes or 1200 sec = 4×1200 = 4800 ft

x = 4800 ft

Since, z² = (500)² + (x + y)²

z² = (500)² + (4500 + 4800)²

z² = 250000 + 86490000

z = √86740000

z = 9313.43 ft

Now we plug in the values in the formula (1)

2(9313.43) = 2(4800 + 4500)(4 + 5)

18626.86 = 18(9300)

feet per sec.

Therefore, both the persons are moving apart by 8.99 feet per sec.

step-by-step explanation: