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calculus

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The position of two particles on the s-axis are s1= cos(t) and s2= cos(t+(symbol for pie)/4)
a. what is the farthest apart the particles ever get?
b. when do the particles collide?

  • calculus -

    I think it would be of more benefit if you posted your thinking or work, and we critiqued it.

  • calculus -

    Well I am in AP Calculus and I don't understand the class to well.

  • calculus -

    difference = y = cos ( t + pi/4) - cos t
    for part a
    take dy/dt and set to 0
    dy/dt = -sin (t+pi/4) + sin t
    0 = sin t - sin (t+pi/4)
    sin t = sin (t+pi/4)
    sin (a+b) =sin a cos b + cos a sin b
    so
    sin t = sin t cos pi/4 + cos t sin pi/4
    sin t = sin t /sqrt 2 + cos t/sqrt 2
    sqrt 2 sin t = sin t + cos t
    (sqrt 2-1) = cos t/sin t = cot t
    cot t = .4142
    t = 67.5 degrees = 1.178 radians
    also in other quadrants where cot t =.4142
    NOW, go back and find y
    for part b,just find when cos (t+pi/4) = cos t

  • calculus -

    Thank You

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