Question

At noon, 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 25km/h. How fast is the distance between the ships changing at 4:00PM?

Answer 1

Can someone explain how to do this problem step by step, please

Answer 2

We need a function describing distance between the ships as a function of the time. The initial distance between the ships is 150km, which occurs at what I will call time t=0. I will call the East direction my positive x and North my positive y. Lets refer everything from the point of view ship A which we will call at rest. Then ship B is approaching A with a horizontal component and moving away from A with a vertical component. Calling d=distance between the ships, we have:
\[d=\sqrt{(150-35t)^2+(25t)^2}\]

Answer 3

is there any way you could draw it?

Answer 4

The draw function on the site is tough

Answer 5

also what would plug into the t variable, time, to get rid of the t

Answer 6

so you can't draw the figure?

Answer 7

Now that we have our function we need to know how fast it changes with time. t=0 is noon here and t=4 would be 4:00pm. We find the derivative of this function (with respect to time) and then plug in t=4 to find out how fast the distance between the ships is changing at 4:00pm.

Answer 8

i'll try to draw it...it's going to look brutal though hehe