Exam 13: Vector Functions

Find the arc length function for the curve defined by for Then use this result to find a parametrization of C in terms of s.

Find satisfying the conditions for

Find and for

A mortar shell is fired with a muzzle speed of 325 ft/sec. Find the angle of elevation of the mortar if the shell strikes a target located 1500 ft away. Round your answer to 2 decimal places.

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

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

Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.

A particle moves with position function . Find the tangential component of the acceleration vector.

A particle moves with position function . Find the normal component of the acceleration vector.

Evaluate the integral.

Find satisfying the conditions for

Find for the function given.

Find a vector function that represents the curve of intersection of the two surfaces: the top half of the ellipsoid and the parabolic cylinder .

The following table gives coordinates of a particle moving through space along a smooth curve. Find the average velocity over the time interval .

What force is required so that a particle of mass has the following position function?.

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

A projectile is fired with an initial speed of and angle of elevation . Find the range of the projectile.

Find the scalar tangential and normal components of acceleration of a particle with position vector

Find the integral

The curves and intersects at the origin. Find their angle of intersection correct to the nearest degree.