1.  Find parametric equations for the curve of the intersection of the elliptical cylinder x^2 / 16 + z^2 / 4 =1 and the parabolic cylinder z = .5 x^2.

 

2.  Find the velocity, the unit tangent vector, the acceleration and the unit normal vectors for the position function r(t) = (t * cos t) i – sqrt(t) j – t * sin(2t) k.

3.  Find its velocity and acceleration in terms of the unit polar vectors u_r and u_theta, for an object is along the curve x = sin( pi/4 * t) , y = -cos( pi/4 t) in the xy plane.

4.  Find the tangential and normal components of an object's acceleration given its position vector r(t) = 4 cos t i +  5 (1-cos t) j + sin t k.

 

5.  Find the position vector R(t) given the velocity vector v(t) = t^(3/2) i – sqrt(t) j + t^2 k, provided the t = 0 position is described by the vector 2 i - j + 5 k.

6.  Give parametric equations for the position of an object moving with angular velocity omega = a t, where t is clock time, around a circle of radius r, centered at the origin.  Calculate the tangential and normal components of its acceleration.