Question

Two boats are leaving port at the same time. Ship A is sailing due east at 40 km/h, and Ship B due south at 30 km/h. How fast are they moving away from each other after 2 hours?

Answer 1

Let's assume that P is the point from where two boat leaves at the same time.

x = distance between Ship A and point P

y = distance between Ship B and point P

z = distance between Ship A and Ship B

dx/dt = 40 km/h and dy/dt = 30km/h

we have to find dz/dt after two hours

As dx/dt = 40 km/h we can say that after two hour,

As dy/dt = 30 km/h we can say that after two hour,

after two hours we have x = 80 and y = 60

Using Pythagorean theorem we can write,

Hence,

distance cannot be negative hence,

Step 2)

Using Pythagorean theorem we can write,

we can write,

we have dx/dt = 40 and dy/dt = 30 and after two hours we have x = 80, y = 60 and z = 100 hence,

Hence we can say that after two hours distance between two ships is increasing at a rate of 50 km/h

we can also write after two hours two ships are moving away from each other at 50 km/h