Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

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?

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• Bryce
Lv 7
1 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

• nbsale
Lv 6
1 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.