Exam 13: Vector Functions

A projectile is fired from a height of 400 ft with an initial speed of 200 ft/sec and an angle of elevation of . a.What are the scalar tangential and normal components of acceleration of the projectile? b.What are the scalar tangential and normal components of acceleration of the projectile when the projectile is at its maximum height?

Find the unit tangent vector for at

Sketch the curve of the vector function and indicate the orientation of the curve.

Find for the function given.

Find the derivative of the vector function.

Find the velocity, acceleration, and speed of an object with position function for Sketch the path of the object and its velocity and acceleration vectors.

Find a vector function that represents the curve of intersection of the two surfaces: The circular cylinder and the parabolic cylinder .

Find the velocity of a particle that has the given acceleration and the given initial velocity.

Find a vector function describing the curve of intersection of the cylinder and the plane

If and , find .

Find the velocity, acceleration, and speed of an object with position function for Sketch the path of the object and its velocity and acceleration vectors.

Let C be a smooth curve defined by , and let and be the unit tangent vector and unit normal vector to C corresponding to t. The plane determined by T and N is called the osculating plane. Find an equation of the osculating plane of the curve described by at

Find the speed of a particle with the given position function.