I am stuck on a math problem. Can someone please help me?
At noon, ship A is 150 km west of ship B. Ship A is sailing east at 35km/h and ship B is sailing north at 25 km/h. How fast is the distance between the ships changing at 4:00 PM?
- BryceLv 71 month ago
D²= x² + y²
D*dD/dt= x*dx/dt + y*dy/dt
D= √(10² + 100²)≈ 100.50 km
100.5*dD/dt= 10*35 + 100*25
dD/dt≈ 28.36 km/h
- nbsaleLv 61 month ago
Set up a coordinate system and place the ships in it based on their positions at noon (t=0).
E.g., you could say B is at (0,0), and A is at (-150,0).
Write down the equations that describe the x and y coordinates of the ships at time t, based on their initial positions, and their speeds.
Those will look like, for ship A, (a constant + xA(t), a constant + yA(t))
For Ship B, (a constant + xB(t), a constant + yB(t))
Find the distance between them at time t, d(t) = sqrt[ (difference in x coord at t)^2 + (difference in y coord at t)^2 ]
Take the derivative d'(t) and evaluate d'(4) to get the answer.
Drawing a good diagram of where the ships are and where they are headed should help make it easier to visualize the problem.