Question

At 2 P.M., ship A is 150 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 25 km/h. How fast is the distance between the ships changing at 6 P.M.? (Round your answer to one decimal place.)

Answer 1

Answer:

The distance between the ships changing at 6PM is 21.29Km/h

Explanation:

Ship A is sailing east at 35Km/h and ship B is sailing West at 25Km/h

Given

dx/dt= 35

dy/dt= 25

dv/dt= ???? at t= 6PM - 2PM= 4

Therefore t=4

We know ship A travels at 150km in the x-direction and Ship A at t=4 travels at 4.35 Which is 140 also in x-direction

So, we use:

$D^2 = (150 - x)^2 + y^2$;

$D^2 = (150 - 140)^2 + y^2$

But ship B travels at t=4, at 4.25 =100 in the y-direction

so, let's use the equation:

$D^2 = 10^2 + 100^2$

$= D= sqrt*(10 + 100)$

Lets use 2DD' = 2xx' + 2yy'

Differentiating with respect to t we have:

D•d(D)/dt = -(10)•dx/dt + 100•dy/dt

=100.5 d(D)/dt = (-10)•35 + (100)•25

When t=4, we have x=(140-150) =10 and y=100

$= D = sqrt*(10^2 + 100^2)$

=100.5

= 100.5 dD/dt = 10.35 +100.25

= dD/dt = 21.29km/h