calculus

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A rocket rises vertically from a point on the ground that is 100m from an observer at ground level. The observer notes that the angle of elevation is increasing at a rate of 12∘per second when the angle of elevation is 60∘. Find the speed of the rocket at that instant. Hint: remember to use radians.

  • calculus -

    make a diagram.
    you should have a right-angled triangle, where the angle of elevation is Ø, the adjacent is 100 and the opposite is h, the height of the rocket.

    tanØ = h/100
    h = 100tanØ
    dh/dt = 100sec^2 Ø (dØ/dt)

    when Ø = 60° or π/3 rad
    dØ/dt = 12°/sec or 12π/180 rad/sec = π/15 rad/sec

    sub into the dh/dt equation and you are done

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