Download ch3-Projectile Motion1

10/28/2014
Projectile Motion
• Horizontal: ax=0
Projectile Motion
What kind of motion is this?
Draw the velocity vectors and strobe photo
• Vertical: ay=9.8 m/s2
Phy 114
Eyres
What kind of motion is this?
Draw the velocity vectors and strobe photo
Projectile Motion
Conceptual Exercise 3.7: Throwing a
ball
• You throw a tennis ball as a projectile. Arrows
represent the ball's instantaneous velocity and
acceleration and the force or forces exerted
on the ball by other objects when at the three
positions shown in the diagram.
Projectile Motion
Quantitative analysis of projectile motion:
Acceleration
• The equations of motion for velocity and
constant acceleration are used to analyze
projectile motion quantitatively.
• The x-component (in the horizontal direction)
of a projectile's acceleration is zero.
• The y-component (in the vertical direction) of
a projectile's acceleration is –g.
– The force is mg—the force of gravity that Earth
exerts on the projectile.
© 2014 Pearson Education, Inc.
© 2014 Pearson Education, Inc.
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10/28/2014
Complete for Vi=40 m/s @ 25° from
150-m cliff
Time
0
Velocity x
(horiz)
X position
Velocity y
(vert)
Vi=40 m/s @ 25° from 150-m cliff
Y position
y vs. x
300
0
200
1
100
0
y position (m)
2
3
4
5
0
200
300
400
500
600
-200
-300
-400
6
-500
7
-600
8
-700
-800
9
•
•
•
•
•
•
•
100
-100
x (m)
Vi=40 m/s @ 25° from 150-m cliff
Solving Projectile Motion Problems
Sketch the x vs t graph
Sketch the y vs t graph
Sketch the vx vs t graph
Sketch the vy vs t graph
Sketch the ax vs t graph
Sketch the ay vs t graph
What can you read from the coordinate, slope,
or area on each graph?
• Draw Motion Diagrams
State the Problem
• Underline or highlight the question(s).
An object is launched with an initial velocity of
40m/s@25° from a cliff that is 150 m above
the valley floor. How long does if take to reach
the ground? How far away from the base of
the cliff does it land?
– You have two of them, horizontal and vertical
– Think about chapter 2, you have constant motion
and free fall.
• Write your equations
– You have two sets, horizontal and vertical
– Same equations as in chapter 2!
• Plug in your known values and solve
Problem Solution Plan
• Plan: What principle, concept or set of
equations might be useful for this problem?
• Hint: How is this motion different than that
from Linear Motion?
Projectile motion can be simplified by breaking
apart into components
Constant in x direction.
a=9.8 m/s2 down in y dir.
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Problem Solution Plan
Problem Solution Plan
• Constant in x direction.
• Constant in y direction.
Solve for Vi
Solve for Vi
vix = 40 ms (cos 25°)
v
Constant
vix = 36.25 ms
a
v
v
x=0
v = 36.25 m/s
t=0
a=0
v
viy = 40 ms (sin 25°)
viy = 16.9
x=
v = 36.25 m/s
t=
m
s
a
v
a = -9.8 m/s2
y = 150 m
v = +16.9 m/s
t=0
Freefall
y =0
v=
t=
Quantitative analysis of projectile motion:
Using our kinematics equations
Solve
xcompone
nt of
motion
vx =
∆x
∆t
y-component of
motion
vy =
ay =
x-component
of motion
vy =
∆y
∆t
∆v y
∆t
1
∆x = viy t + a y t 2
2
1
− 150m = 16.9 ms t + (−9.8 sm2 )t 2
2
0 = (−4.9 sm2 )t 2 + 16.9 ms t + 150m
y-component of motion
36.25 ms =
∆x
∆t
− 150m
∆t
ay =
∆v y
∆t
1
− 150m = 16.9 ms t + (−9.8 sm2 )t 2
2
− b ± b 2 − 4ac
2a
t = 7.5s
∆x = 273m
t=
• Equation (3.8y) can be used to determine the
time interval for the projectile's flight.
• Equation (3.8x) can be used to determine how far
the projectile travels in the horizontal direction
during that time interval.
© 2014 Pearson Education, Inc.
Answer and Evaluate
• Answer the question(s) that was asked.
How long does if take to reach the ground?
7.5 seconds
How far away from the base of the cliff does it land?
273 meters
• Evaluate
Example 3.9: Shot from a cannon
• Stephanie Smith Havens is to be shot from an 8-m-long
cannon at 100 km/h. The barrel of the cannon is oriented 45°
above the horizontal. She hopes to be launched so that she
lands on a net that is 40 m from the end of the cannon barrel
and at the same elevation (our assumption).
• Estimate the speed with which she needs to leave the cannon
to make it to the net.
Is the magnitude reasonable? Check your estimated
answer from the chart.
Count 7 seconds and think about how high 150 m is.
© 2014 Pearson Education, Inc.
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10/28/2014
Write the equations for Example 3.9
xcompone
nt of
motion
vx =
∆x
∆t
y-component of
motion
vy =
ay =
x-component
of motion
y-component of motion
∆y
∆t
∆v y
∆t
1
∆x = viy t + a y t 2
2
4