6 Motion in Two Dimensions
BIGIDEA
Write the Big Idea for this chapter.
Use the “What I Know” column to list the things you know about the Big Idea. Then list the
questions you have about the Big Idea in the “What I Want to Find Out” column. As you read the
chapter, fill in the “What I Learned” column.
W
What I Want to Find Out
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K
What I Know
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L
What I Learned
6 Motion in Two Dimensions
1 Projectile Motion
MAINIDEA
Write the Main Idea for this section.
REVIEW VOCABULARY
Recall and write the definition of the Review Vocabulary term.
motion diagram
motion diagram
NEW VOCABULARY
projectile
trajectory
Use your book to define each term.
projectile
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trajectory
1 Projectile Motion (continued)
Student Edition, pp. 152–154
Draw an illustration of a softball gently tossed from one player to
another. Label the projectile and the trajectory in the illustration.
Identify the only force acting on a tossed ball (ignoring air resistance).
Copyright © McGraw-Hill Education. Permission is granted to reproduce for classroom use.
Compare the horizontal motion and the vertical motion of the balls in
Figure 2.
GET IT?
Explain why a dropped object has the same vertical velocity
as an object launched horizontally.
Complete the sentences to make them true.
In a horizontally launched projectile, the x- and y-components can be
treated
. The resultant vectors of the projectile are
to a
.
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1 Projectile Motion (continued)
Student Edition, pp. 154–156
Describe a scenario in which the diagram in Figure 3 could be used to
describe the motion of an object.
GET IT?
Explain why the horizontal motion of a projectile is constant.
Explain why a horizontally launched projectile has a parabolic shape.
Identify two important components in the path of an object launched at
an angle.
GET IT?
Identify At what point of a projectile’s trajectory is its vertical
velocity zero?
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Describe the significance of symmetry in the path of an object launched
straight up in the air.
1 Projectile Motion (continued)
Student Edition, p. 157
Use with Example Problem 2.
Use this column for
scratch work and
sketches.
TRY IT!
Problem
THE FLIGHT OF A BALL A ball is launched at 5.5 m/s at 76° above the
horizontal. It starts and lands at the same distance from the ground. What
are the maximum height above its launch level and the flight time of the
ball?
1. ANALYZE AND SKETCH THE PROBLEM
KNOWNS
yi =
θ=
=?
vi =
ay =
=?
vy, max =
2. SOLVE FOR THE UNKNOWNS
Find the y-component of vi.
Use symmetry to find the y-component of vf.
Copyright © McGraw-Hill Education. Permission is granted to reproduce for classroom use.
UNKNOWNS
Solve for the maximum height.
Solve for the time to return to the launching height.
3. EVALUATE THE ANSWER
• Are the magnitudes realistic?
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1 Projectile Motion (continued)
Student Edition, p. 158
Draw three pictures below showing how moving air affects water flowing
from a water hose. Use vectors to show motion.
No Effect from Air
Force of Air that Increases Velocity
Force of Air that Decreases Velocity
How does the MAINIDEA for this section relate to the chapter’s BIGIDEA?
REVIEW IT !
7. MAINIDEA Two baseballs are pitched horizontally from the same height but at
different speeds. The faster ball crosses home plate within the strike zone, but the
slower ball is below the batter’s knees. Why do the balls pass the batter at different
heights?
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Copyright © McGraw-Hill Education. Permission is granted to reproduce for classroom use.
SUMMARIZE
1 Projectile Motion (continued)
8. Free-Body Diagram An ice cube slides without friction across a table at a constant velocity. It slides
off the table and lands on the floor. Draw free-body and motion diagrams of the ice cube at two
points on the table and at two points in the air.
9. Projectile Motion A tennis ball is thrown out a window 28 m above the ground at an
initial velocity of 15.0 m/s and 20.0° below the horizontal. How far does the ball move
horizontally before it hits the ground?
Copyright © McGraw-Hill Education. Permission is granted to reproduce for classroom use.
10. Projectile Motion A softball player tosses a ball into the air with an initial velocity of
11.0 m/s, as shown in Figure 7. What will be the ball’s maximum height?
50°
Figure 7
11. Critical Thinking Suppose an object is thrown with the same initial velocity and
direction on Earth and on the Moon, where the acceleration due to gravity is one-sixth
its value on Earth. How will vertical velocity, time of flight, maximum height, and
horizontal distance change?
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