Larson_Calculus_10e ch12sec05
MULTIPLE CHOICE
1. Find the length of the plane curve given below.
a.
20
b.
9
c.
17
d.
19
e.
18
2. 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.
3. 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 maximum height. Round your answer to the nearest integer.
a.
66 feet
b.
65 feet
c.
53 feet
d.
56 feet
e.
61 feet
4. 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
5. A baseball is hit 5 feet above the ground at 95 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.
270.8 feet
b.
298 feet
c.
293.7 feet
d.
239.1 feet
e.
330.7 feet
6. Find the arc length for over the interval . Round your answer to two
decimal places.
a.
67.63
b.
73.37
c.
79.40
d.
49.75
e.
62.97
7. Find the length of the space curve given below.
a.
b.
c.
d.
e.
8. Find the curvature K of the curve given below.
a.
b.
c.
d.
e.
9. 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
10. 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
11. 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
12. 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
13. Find the point on the curve at which the curvature K is a maximum.
a.
b.
c.
d.
e.
14. Find the point on the curve given below at which the curvature K is zero.
a.
b.
c.
d.
e.
15. 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
16. 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