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?
4 answers
I think it would be of more benefit if you posted your thinking or work, and we critiqued it.
Well I am in AP Calculus and I don't understand the class to well.
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
Thank You
3 answers