Deck 12: Section 5: Vector-Valued Functions

Question 1

Find the curvature K of the curve at the point . Round your answer to three decimal places.

A) 7.286
B) 9.952
C) 0.021
D) 0.014
E) 0.009

Answer 1

0.009

Question 2

A 5700-pound vehicle is driven at a speed of 25 miles per hour on a circular interchange of radius 90 feet. To keep the vehicle from skidding off course, what frictional force must the road surface exert on the tires? Round your answer to one decimal place.

A) 2,670.2 lb
B) 3,337.8 lb
C) 2,993.5 lb
D) 2,660.9 lb
E) 3,503.9 lb

Answer 2

2,660.9 lb

Question 3

Find the length of the plane curve given below.

A)
B)
C)
D)
E)

Answer 3

Question 4

The smaller the curvature in a bend of a road, the faster a car can travel. Assume that the maximum speed around a turn is inversely proportional to the square root of the curvature. A car moving on the path (x and y are measured in miles) can safely go 25 miles per hour at . How fast can it go at ? Round your answer to two decimal places.

A) 259.31 mi/h
B) 149.71 mi/h
C) 119.77 mi/h
D) 75.30 mi/h
E) 299.42 mi/h

Question 5

Find the length of the plane curve given below.

A) 1620
B) 648
C) 1296
D) 3260
E) 6480

Question 6

Find the curvature of the plane curve at . Round your answer to three decimal places.

A) 0.498
B) 0.332
C) 0.015
D) 0.005
E) 0.003

Question 7

Find the curvature K of the curve at the point . Round your answer to three decimal places.

A) 0.883
B) 0.994
C) 0.019
D) 0.012
E) 0.017

Question 8

Find the length of the space curve given below.

A)
B)
C)
D)
E)

Question 9

Find the length of the plane curve given below.

A) 20
B) 9
C) 17
D) 19
E) 18

Question 10

A baseball is hit 5 feet above the ground at 140 feet per second and at an angle of with respect to the ground. Find the vector-valued function for the path of the baseball.

A)
B)
C)
D)
E)

Question 11

Find the point on the curve at which the curvature K is a maximum.

A)
B)
C)
D)
E)

Question 12

Find the curvature K of the curve given below.

A)
B)
C)
D)
E)

Question 13

Find the curvature K of the curve given below.

A)
B)
C)
D)
E)

Question 14

Find the radius of curvature of the plane curve at . Round your answer to three decimal places.

A) 24.694
B) 85.333
C) 28.133
D) 34.510
E) 37.510

Question 15

A baseball is hit 3 feet above the ground at 80 feet per second and at an angle of with respect to the ground. Find the range. Round your answer to one decimal place.

A) 203 feet
B) 259.5 feet
C) 275.7 feet
D) 386.6 feet
E) 215.6 feet

Question 16

Find the point on the curve given below at which the curvature K is zero.

A)
B)
C)
D)
E)

Question 17

Find the arc length for over the interval . Round your answer to two decimal places. 2 5

A) 46.09
B) 48.10
C) 26.49
D) 40.98
E) 38.15

Question 18

A baseball is hit 5 feet above the ground at 130 feet per second and at an angle of with respect to the ground. Find the maximum height. Round your answer to the nearest integer.

A) 159 feet
B) 137 feet
C) 166 feet
D) 150 feet
E) 146 feet

Question 19

A baseball is hit 3 feet above the ground at 90 feet per second and at an angle of with respect to the ground. Find the arc length of the trajectory. Round your answer to one decimal place.

A) 261.6 feet
B) 212.8 feet
C) 240.8 feet
D) 294.8 feet
E) 266.4 feet