Deck 13: Vector Functions

Question 1

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

A)
B)
C)
D)
E)

Answer 1

Question 2

The position function of a particle is given by When is the speed a minimum?

A)
B)
C)
D)
E)

Answer 2

Question 3

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

Answer 3

Question 4

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

A) km
B) km
C) km
D) km
E) km

Question 5

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

A)
B)
C)
D)
E)

Question 6

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

A) ,
B) ,
C) ,
D) ,

Question 7

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

A)
B)
C)
D)
E)

Question 8

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.

Question 9

A force with magnitude N acts directly upward from the xy-plane on an object with mass kg. The object starts at the origin with initial velocity . Find its position function.

A)
B)
C)
D)
E)

Question 10

Find the acceleration of a particle with the following position function.

A)
B)
C)
D)
E)

Question 11

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

Question 12

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.

A)
B)
C)
D)

Question 13

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

A)
B)
C)
D)
E)

Question 14

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

A)
B)
C)
D)
E)

Question 15

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

A)
B)
C)
D)
E)

Question 16

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

A)
B)
C)
D)
E)

Question 17

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

A)
B)
C)
D)
E)

Question 18

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

A)
B)
C)
D)

Question 19

A particle moves with position function . Find the acceleration of the particle.

Question 20

A ball is thrown at an angle of to the ground. If the ball lands m away, what was the initial speed of the ball? Let .

A)
B)
C)
D)
E)

Question 21

For the curve given by , find the unit normal vector.

A)
B)
C)
D)
E)None of these

Question 22

Find the velocity, acceleration, and speed of an object with position vector .

Question 23

Find the curvature of the curve .

A)
B)
C)
D)

Question 24

A projectile is fired from ground level with an initial speed of 1100 ft/sec and an angle of elevation of
a.Find the range of the projectile.
b.What is the maximm height attained by the projectile?
c.What is the speed of the projectile at impact?
Round your answers to the nearest integer.

Question 25

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.

Question 26

Find the unit tangent and unit normal vectors and for the curve C defined by

Question 27

Reparametrize the curve with respect to arc length measured from the point where in the direction of increasing .

A)
B)
C)
D)
E)

Question 28

Find the curvature of the curve .

A)0
B)11
C)1
D)

Question 29

Find the length of the curve

A)
B)
C)
D)

Question 30

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

A)
B)
C)
D)

Question 31

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?

Question 32

Find the curvature of .

A)
B)
C)
D)
E)

Question 33

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

Question 34

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.

Question 35

Find the length of the curve

A)
B)
C)
D)

Question 36

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.

Question 37

Find the unit tangent and unit normal vectors and for the curve C defined by Sketch the graph of C, and show and for

Question 38

Find the velocity, acceleration, and speed of an object with position vector .

Question 39

Find the length of the curve

A)
B)
C)
D)

Question 40

Find the velocity and position vectors of an object with acceleration initial velocity and initial position

Question 41

The figure shows a curve given by a vector function . Choose the correct expression for .

A)
B)
C)
D)
E)

Question 42

The curvature of the curve given by the vector function is Use the formula to find the curvature of at the point .

A)
B)
C)
D)
E)

Question 43

Find the point(s) on the graph of at which the curvature is zero.

Question 44

If , evaluate .

A)
B)
C)
D)
E)

Question 45

The helix intersects the curve at the point . Find the angle of intersection.

A)
B)
C)
D)
E)None of these

Question 46

Use Simpson's Rule with n = 4 to estimate the length of the arc of the curve with equations , from to . Round your answer to four decimal places.

A)
B)
C)
D)
E)None of these

Question 47

The torsion of a curve defined by is given by Find the torsion of the curve defined by .

A)
B)
C)
D)

Question 48

Find satisfying the conditions for

A)
B)
C)
D)

Question 49

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

A)
B)
C)
D)

Question 50

Find equations of the normal plane to at the point (2, 4, 8).

Question 51

Evaluate the integral.

A)
B)
C)
D)
E)

Question 52

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.

Question 53

Find satisfying the conditions for

A)
B)
C)
D)

Question 54

At what point on the curve is the normal plane parallel to the plane ?

A)
B)
C)
D)
E)

Question 55

Find the unit tangent vector .

A)
B)
C)
D)
E)

Question 56

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

A)
B)
C)
D)

Question 57

Find the unit tangent vector for at

A) i j k
B)
C) i + j + k
D)

Question 58

If , find .

A)
B)
C)
D)
E)

Question 59

Find the integral

A)
B)
C)
D)

Question 60

Find if and .

A)
B)
C)
D)
E)

Question 61

Find the limit.

A)
B)
C)
D)
E)

Question 62

Find the point of intersection of the tangent lines to the curve , at the points where and .

Question 63

Find the derivative

Question 64

Let . Find the domain of .

A)
B)
C)
D)
E)

Question 65

Find and for

Question 66

Find for the function given.

Question 67

Find if and .

Question 68

Find the domain of the vector function .

A)
B)
C)
D)

Question 69

Find the integral

Question 70

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

A)
B)
C)
D)
E)

Question 71

Find the derivative of the vector function.

Question 72

Find and for

Question 73

Find for the function given.

A)
B)
C)
D)
E)

Question 74

Find an expression for .

Question 75

Find the domain of the vector function .

A)
B)
C)
D)

Question 76

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

Question 77

Find the unit tangent vector for the curve given by .

A)
B)
C)
D)
E)None of these

Question 78

Given
a.Find and .
b.Sketch the curve defined by r and the vectors and on the same set of axes.

Question 79

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

A)
B)
C)
D)
E)

Question 80

If and , find .