Deck 12: Section 4: Vector-Valued Functions

Question 1

Find the unit tangent vector for the line tangent to the space curve at point .

A)
B)
C)
D)
E)

Answer 1

Question 2

Find at time for the plane curve . Round your answer to three decimal places.

A) -40.625
B) -39.209
C) -111.667
D) -46.016
E) -43.988

Answer 2

-46.016

Question 3

Find at time for the space curve . Round your answer to three decimal places.

A) 0.062
B) 0.071
C) 0.659
D) 0.000
E) 0.753

Answer 3

0.000

Question 4

Find the principle unit normal vector to the curve given below at the specified point.

A)
B)
C)
D)
E)

Question 5

Find at time for the plane curve . Round your answer to three decimal places.

A) 6.581
B) 4.818
C) 3.407
D) 2.154
E) 4.962

Question 6

Find the principle unit normal vector to the curve given below at the specified point.

A)
B)
C)
D)
E)

Question 7

Use the result, "the tangential and normal components of acceleration for a projectile fired at an angle with the horizontal at an initial speed of are and respectively.", to find the tangential component of acceleration for a projectile fired at an angle of with the horizontal at an initial speed of 152 feet per second. What is the component when the projectile is at its maximum height?

A) 76
B) 32
C) 16
D) 152
E) 0

Question 8

Find at time for the space curve .

A) 16
B) 0
C) 5
D) 25
E) 4

Question 9

Find the unit tangent vector to the curve given below at the specified point.

A)
B)
C)
D)
E)

Question 10

Find at time for the plane curve . Round your answer to three decimal places.

A) 11.077
B) 7.310
C) 11.797
D) 5.898
E) 5.538

Question 11

Find the unit tangent vector T(t) and then use it to find a set of parametric equations for the line tangent to the space curve given below at the given point.

A)
B)
C)
D)
E)

Question 12

Use the result, "the tangential and normal components of acceleration for a projectile fired at an angle with the horizontal at an initial speed of are and respectively.", to find the normal component of acceleration for a projectile fired at an angle of with the horizontal at an initial speed of 148 feet per second. What is the component when the projectile is at its maximum height?

A) 0
B) 74
C) 148
D) 32
E) 16

Question 13

Verify that the space curves intersect at the given values of the parameter. Find the angle between the tangent vectors at the point of intersection. , ,

A)
B)
C)
D)
E)

Question 14

Find the principle unit normal vector to the curve given below at the specified point.

A)
B)
C)
D)
E)

Question 15

Find at time for the space curve . Round your answer to three decimal places.

A) 0.970
B) 0.465
C) 0.930
D) 1.814
E) 1.060

Question 16

Find a set of parametric equations for the tangent line to the graph at and use the equations for the line to approximate .

A)
B)
C)
D)
E)

Question 17

Because of a storm, ground controllers instruct the pilot of a plane flying at an altitude of 1.6 miles to make a turn and climb to an altitude of 1.8 miles. The model for the path of the plane during this maneuver is where t is the time in hours and is the distance in miles. Determine the speed of the plane. Round your answer to the nearest integer.

A) 50 mi/h
B) 16 mi/h
C) 54 mi/h
D) 34 mi/h
E) 79 mi/h

Question 18

Find the unit tangent vector to the curve given below at the specified point.

A)
B)
C)
D)
E)

Question 19

Find at time for the space curve . Round your answer to three decimal places.

A) 0.781
B) 0.724
C) 0.343
D) 0.686
E) 0.649

Question 20

Find at time for the plane curve . Round your answer to three decimal places.

A) 18.724
B) 23.792
C) 22.264
D) 15.179
E) 22.764