Two parallel paths 17 m apart run east–west through the woods. Brooke walks east on one path at 4 km/h, while Jamail walks west on the other path at 7 km/h. If they pass each other at time ????=0, how far apart are they 11 s later, and how fast is the distance between them changing at that moment?

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DeniceSandidge DeniceSandidge · Answer 1 · 2019-10-31T07:30:26+01:00

Answer:

D(11) = 37.660 m

dD/dt = 2.7260 m/s

Explanation:

given data

two path apart = 17 m

walks east one path = 4 km/h = 1.111 m/s

walks west other path = 7 km/h = 1.944 m/s

pass each other time t = 0

solution

we consider here east is the positive direction and west is the negative direction

so that

the east - west distance between them is = 1.111 + 1.944 = 3.055 m/s

and

the actual distance between them time t is

D(t) = [tex]\sqrt{(3.055 t)^2 + 17 ^2}[/tex]

at time 11 s

D(11) = [tex]\sqrt{(3.055 *11)^2 + 17 ^2}[/tex]

D(11) = 37.660 m

and

increase rate is dD/dt

dD/dt = [tex]\frac{0.5(2) t (3.055)^2}{\sqrt{(3.055 t)^2 +17^2}}[/tex]

so for 11 sec

dD/dt = [tex]\frac{0.5(2) 11 (3.055)^2}{\sqrt{(3.055 *11)^2 +17^2}}[/tex]

dD/dt = 2.7260 m/s