12.3 Velocity and Acceleration 721
12.3 Velocity and Acceleration
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. The position vector describes the path of an object moving in
the xy-plane. Sketch a graph of the path and sketch the velocity and acceleration vectors at the point
.
a. d.
b. e.
722 Chapter 12: Vector-Valued Functions
c.
____ 2. The position vector describes the path of an object moving in
space. Find the speed of the object.
a.
b.
c.
d.
e.
____ 3. The position vector describes the path of an object moving in
space. Find the acceleration of the object.
a.
b.
c.
d.
e.
12.3 Velocity and Acceleration 723
____ 4. The position vector describes the path of an object moving in
space. Find the speed of the object.
a. 21
b.
37
c.
93
d. 149
e.
85
____ 5. The position vector describes the path of an object moving in
space. Find the velocity of the object.
a.
b.
c.
d.
e.
____ 6. The position vector describes the path of an object moving in
space. Find the velocity of the object.
a.
b.
c.
d.
e.
724 Chapter 12: Vector-Valued Functions
____ 7. Use the given acceleration function and initial conditions to find the position at time t
= 1.
a.
b.
c.
d.
e.
____ 8. Use the given acceleration function and initial conditions to find the position at time t
= 1.
a.
b.
c.
d.
e.
____ 9. Use the given acceleration function and initial conditions to find the position at time t
= 3.
a.
b.
c.
d.
e.
____ 10. Determine the maximum height of a projectile fired at a height of 6 feet above the
ground with an initial velocity of 700 feet per second and at an angle of above the horizontal. Use
the model for projectile motion, assuming there is no air resistance. Round your answer to three
decimal places.
a. 14,289.757 feet
b. 14,292.757 feet
c. 7,146.378 feet
d. 7,149.378 feet
e. 14,298.757 feet
12.3 Velocity and Acceleration 725
____ 11. Determine the range of a projectile fired at a height of 5 feet above the ground with
an initial velocity of 1000 feet per second and at an angle of above the horizontal. Use the model
for projectile motion, assuming there is no air resistance. Round your answer to three decimal places.
a. 15,627.500 feet
b. 8,137.843 feet
c. 31,252.187 feet
d. 31,254.999 feet
e. 16,268.138 feet
____ 12. A baseball, hit 9 feet above the ground, leaves the bat at an angle of and is caught
by an outfielder 9 feet above the ground and 500 feet from home plate. What is the initial speed of the
ball? Round your answer to two decimal places.
a. 31.62 ft/sec
b. 126.49 ft/sec
c. 189.74 ft/sec
d. 158.11 ft/sec
e. 63.25 ft/sec
____ 13. A baseball, hit 5 feet above the ground, leaves the bat at an angle of and its caught
by an outfielder 5 feet above the ground and 500 feet from home plate. How high does the ball rise?
Round your answer to the nearest integer.
a. 77 feet
b. 10 feet
c. 167 feet
d. 118 feet
e. 23 feet
____ 14. A baseball player at second base throws a ball 87 feet to the player at first base. The
ball is thrown 5 feet above the ground with an initial velocity of 50 miles per hour and at an angle of
above the horizontal. At which height does the player at first base catch the ball? Round your
answer to three decimal places.
a. 7.576 feet
b. 6.676 feet
c. 5.476 feet
d. 6.076 feet
e. 5.576 feet
____ 15. The quarterback of a football team releases a pass at a height of 8 feet above the
playing field, and the football is caught by a receiver 38 yards directly downfield at a height of 4 feet.
The pass is released at an angle of with the horizontal. Find the speed of the football when it is
released. Round your answer to three decimal places.
a. 33.169 feet per second
b. 59.366 feet per second
c. 19.462 feet per second
d. 118.732 feet per second
e. 190.165 feet per second
726 Chapter 12: Vector-Valued Functions
____ 16. The quarterback of a football team releases a pass at a height of 6 feet above the
playing field, and the football is caught by a receiver 42 yards directly downfield at a height of 3 feet.
The pass is released at an angle of with the horizontal. Find the maximum height of the football.
Round your answer to one decimal place.
a. –295.8 feet
b. –194.1 feet
c. –278.9 feet
d. –224.3 feet
e. –197.7 feet
____ 17. The quarterback of a football team releases a pass at a height of 6 feet above the
playing field, and the football is caught by a receiver 34 yards directly downfield at a height of 3 feet.
The pass is released at an angle of with the horizontal. Find the time in seconds the receiver has to
reach the proper position after the quarterback releases the football. Round your answer to one
decimal place.
a. 0.8 second
b. 4.6 seconds
c. 7.8 seconds
d. 1.3 seconds
e. 2.6 seconds
12.3 Velocity and Acceleration 727
12.3 Velocity and Acceleration
Answer Section