Calculus

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at 12 noon ship A is 65 km due north of a second ship B. Ship A sails south at a rate of 14km/hr, and ship B sails west at a rate of 16km/hr. How fast are the two ships approaching each other 1.5 hours later at 1:30pm? Thank You!

  • Calculus -

    Making a sketch for the 12 noon position, placing B at the origin and A 65 units up on the y-axis
    At a time of t hrs after noon,
    let the distance covered by A be 14t
    let the distance covered by B be 16t
    Draw a line between their positions and call it d km

    d^2 = (16t)^2 + (65-14t)^2
    when t = 1.5
    d^2 = 620
    d = √620

    2d dd/dt = 2(16t)(16) + 2(65- 14t)(14)
    dd/dt = (256t + 65 - 196t)/√620
    when t=1.5
    dd/dt = (256(1.5) + 65 - 196(1.5))/√620
    = 6.22 km/h

    check my arithmetic

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