Question

At noon, ship A is 70 km west of ship B. Ship A is sailing south at 40 km/h and ship B is sailing north at 20 km/h. How fast is the distance between the ships changing at 4:00 PM? (Round your answer to one decimal place.)

Answer 1

Answer:

57.6 km per hr

Step-by-step explanation:

Let us assume the horizontal distance between the ship is constant = x

= 70 Km

The ship A sails south at 40km/h is denoted as 40t

The Ship B sails north at 20 km/h is denoted as 20t

Now the vertical distance separating the two ships is

=  20t + 40t

= 60t

And, the Distance between the ship is changing

$D^2 = y^2 + x^2$

As x is constant

$\frac{\partial x}{\partial t} = 0$

Now differentiating

$2D \frac{\partial D}{\partial t} = 2y \frac{\partial y}{\partial t}$

The distance between two ships is at 4

So,  

vertical distance is

$= 60\times 4$

= 240

And, the horizontal distance is 70

$D = \sqrt{240^2 + 70^2} = 250$

$2 \times 250 \frac{\partial D}{\partial T} = 2 \times 240 \times 60$

So, the distance between the ships is  57.6 km per hr