At noon, ship A is 130 km west of ship B. Ship A is sailing east at 30 km/h and ship B is sailing north at 15 km/h. How fast is the distance between the ships changing at 4:00 PM?

Answer 1

ship A is 130 km west of ship B, at noon

A goes east at 30 kmh for 4 hours, going 120 km

B goes north at 15 kmh for 4 hours, going 60 km

It helps to graph where they are, with the origin (0,0) as B's initial position and (-130,0) as A's initial position

in 4 hours B is at (0,60) and A is at (-10,0)

at noon, they were 130 km apart

at 4pm they are sqr(3600+100)=sqr3700= about 60.83 km apart

Let d = the distance they are apart

d^2 = b^2 + a^2 where a= distance from A to the origin

and b = distance from B to the origin

take the derivative with respect to time

2dd' = 2bb' + 2aa' at time t=4, d=60.83, b=10, b'=30, a=60,a'=15

dd' = bb' + aa'

60.83 d' = 10(30) + 60(15)

d' =(300+900)/60.83 = 1200/60.83

d' = rate of change of the distance between them at 4pm

d'= 120/6.083

d' = about 19.7 kmh