An arrow shot from a bow travels along a curved trajectory given by the set of points satisfying

where

a. find the unit tangent vector T to this curve as a function of t

b. find unit nomrla vector N to this curve as function of t

c. taking {T,N} as an orthonormal basis defininf the orientation of the arrow, find the angle through which the arrow rotates from t=3 to t=4

d. using this angle, or otherwise, find a transformation matrix that maps the basis at time t=3 to the basis at time t=4

k so

so a.

b.

c. i tried evaluating the values

but i don't know if this is usefull or where to go from there.

d. No idea.