Find aT and aN as a function of t rt 7t 6 cos t 6 sin t aT

Find a_T and a_N as a function of t. r(t) = 7t, 6 cos t, 6 sin t a_T = a_N =

Solution

r(t) = < 7t , 6 cos t , 6 sin t >

r\'(t)= < 7 , -6 sin t , 6 cos t >

llr\'(t)ll = sqrt(49+36cos²t+36sin²t) = sqrt(49+36) =sqrt(85)

a_T = < 7/sqrt(85) , -6/sqrt(85) sin t , 6/sqrt(85) cos t >

a\'_T = < 0 , -6/sqrt(85) cos t , -6/sqrt(85) sin t >

ll a\'_T ll = sqrt( 36/85 cos²t + 36/85 sin²t ) = sqrt(36/85) = 6 / sqrt(85)

a_N = < 0 , - cos t , - sin t >