Asked by Barbara
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?
a. what is the farthest apart the particles ever get?
b. when do the particles collide?
Answers
Answered by
bobpursley
I think it would be of more benefit if you posted your thinking or work, and we critiqued it.
Answered by
Barbara
Well I am in AP Calculus and I don't understand the class to well.
Answered by
Damon
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
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
Answered by
Barbara
Thank You
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