Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

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?

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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

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  • 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.

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