Worksheet D

NAME
8-3
DATE
PERIOD
Word Problem Practice
Dot Products and Vector Projections
1. SUBMARINES The path of a submarine
can be described by the vector v = 〈8, 3〉.
If the submarine then changes direction
and travels along the vector u = 〈2, 5〉,
what is the distance traveled by the
submarine?
4. TRAVELING A pilot is carrying a bag
weighing 150 newtons up a flight of
stairs. The staircase covers a horizontal
distance of 8 meters and a vertical
distance 7.5 meters.
a. What is the length of the staircase?
2. TARGETS Two clay pigeons are thrown
at the same time. If the path of the clay
pigeons can be represented by the vectors
p = 〈42, 58〉 and c = 〈59, 73〉, what was
the measure of the angle between the clay
pigeons?
b. What is the measure of the angle
made by the staircase?
c. How much work is done by the pilot?
3. BOATING Shea is pulling a boat along
a dock using a rope. She exerts a force
of 200 newtons on the rope and pulls the
boat 10 meters.
a. Determine the amount of work done
if the angle of the rope is at 40° with
the horizontal; 90° with the horizontal.
60°
6. SCAVENGER HUNT During a
scavenger hunt, Alexis and Marty go in
different directions. If the path that
Alexis takes can be represented by
〈9, 18〉 and the path taken by Marty
can be represented by 〈-15, 12〉, who
travels the farthest distance?
b. Use your results from part a to explain
why as the angle increases the work
decreases.
Chapter 8
18
Glencoe Precalculus
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. CARNIVALS A slide at a carnival has
an incline of 60°. A 50-pound girl gets
part way down the slide and stops.
Ignoring the force of friction, what is
the magnitude of the force that is
required to keep her from sliding
down farther?