•cover the section on, “motion in two or three dimensions.” skip “motion...
TRANSCRIPT
Planning Ahead
• Cover the section on, “Motion in Two or
Three Dimensions.” Skip “Motion in a
Circle” and “Relative Velocity”
• Level III: Kinematics on Wednesday.
• Homework due Wed-2-26-20.
Lecture Outline• I. Projectile Motion
• Level II: Kinematics
Goals• Understand that projectile motion is a two
motion problem: linear motion in the x-
direction and linear motion in the y-direction.
Learn from your Mistakes
If you hit the ball incorrectly, you should know why you hit the
ball incorrectly, and know how to correct your mistake.
33. Find the Displacement vs. time graph?
34. Find the Acceleration vs. time graph?
Recall: Theory of Freefall Motion
• Newton’s second law, states that the weight force of the object causes the object to accelerate.
iyvgttv
iiy
2 ytvgt2
1ty
ga y
Free-Fall Assessment• 1. A ball, starting from rest, is dropped from the top of
a building 100 m high. After what time interval does
the egg strike the ground?
• 2. A ball is thrown upward with an initial velocity of
44.3 m/s. What maximum height does the ball go
from the ground?
• 3. A ball is thrown downward with a initial speed of
14.7 m/s from the top of a building of height 89 m.
After what interval does the ball strike the ground?
GraphsCase 1 Case 2 Case 3
m100ts
m8.9
2
1ty 2
2
ts
m3.44t
s
m8.9
2
1ty 2
2
m89ts
m7.14t
s
m8.9
2
1ty 2
2
Graph Interpretation
Review Concept
If a person is tossed upward, that person would
feel weightless between
A. A to B
B. B to C
C. A to C
D. All of the above
Kinematics Equation
𝑥𝑓 = 𝑣𝑖𝑡 + 𝑥𝑖
𝑣𝑓 = 𝑣𝑖
If a = 0
then
If a = constant
then
𝑥𝑓 =1
2𝑎𝑥𝑡
2 + 𝑣𝑖𝑡 + 𝑥𝑖
𝑣𝑓 = 𝑎𝑥𝑡 + 𝑣𝑖
From Newton’s 2nd Law F = ma:
The numbers put into the equation
come from the sketch.
Projectile Drill/Due Today
I. Projectile Motion
(x, y)
x
y
Projectile Equations• Projectile motion, constant acceleration,
ay = -9.8m/s2, ax = 0. Newton’s 2nd Law.
iixf xtvx iiy
2
2f ytvts
m9.4y
iy2fy vts
m8.9v
cosvv iix
sinvv iiy
iv
Projectile Drill/Due Today
• A ball is thrown horizontally at 40 m/s from
a height of 100 m and lands on a platform
20 m high. Draw the sketch of this problem.
• How long does it take the ball to hit the land
on the platform?
• How far horizontally must the platform be?
Theory of Projectile Motion
jmgw
0Fx
yy mamgF
0a x
ga y
jmgw
Newton’s 1st Law
Newton’s 2nd Law
Projectile Motion Facts• “In order to analyze projectile motion, we
separate the motion into two parts, the x (or
horizontal) motion and the y (or vertical)
motion, and solve each part separately.
Experiment shows that the horizontal and
vertical motions are independent of each
other. This means neither the x motion nor the
y motion is changed by the presence of the
other.”
Critical Thinking Drill/Due Today
• When bullet A is fired horizontally to the ground,
bullet B is dropped from the same height. Which of
the following is true?
• (a) bullet A reaches the ground before bullet B
• (b) bullet A and B reach the ground at the same time
• (c ) bullet B reaches the ground before bullet A
• (d) it depends on the height of the drop
Critical Thinking Drill/Due Today
• A person in a moving train drops a ball and measures
the fall time to be 1 second. A person on the ground,
watching the train go by also sees the person drop the
ball, she measures the fall time to be
• (a) more than 1 second
• (b) exactly 1 second
• (c ) less than 1 second
• (d) cannot be determined
Drop Object in Moving Train
Drill Solution
• When bullet A is fired horizontally to the
ground, bullet B is dropped from the same
height. Which of the following is true? (a)
bullet A reaches the ground before bullet B,
(b) bullet A and B reach the ground at the
same time, or (c ) bullet B reaches the
ground before bullet A. State your
reasoning.
Concept Drill
A ball launcher travels horizontally and launches a yellow
ball upwards. Does the yellow ball land
a.) behind the launcher
b.) on the launcher
c.) in front of the launcher
d.) not enough information to determine
A hunter points his rifle directly at a coconut that he wishes to shoot off a tree. It so happens that the coconut falls from the tree at the exact instant the hunter pulls the trigger. Consequently,
A. the bullet passes above the coconut.
B. the bullet hits the coconut.
C. the bullet passes beneath the coconut.
D. This wasn’t discussed in Chapter 4.
Review Drill/Due Today
• A ball is dropped from a height of 2 m.
How long does it take the ball to hit the
ground? [Note: this concept occurs a lot in
class, make sure you understand this. If not
memorize this].
Solution
m0.2yi
0yf
0viy
?vfy
2ys
m8.9a
o
mts
m0.29.40 2
2 t
s
m8.9v
2fy
?t
Solution
m0.2ts
m9.40 2
2 t
s
m8.9v
2fy
s639.0
s
m9.4
m0.2t
2
Visualization Templateixv
0t i t
fxv
xa xa)0,0(
iix
2
xf xtvta2
1x
ixxfx vtav
ix fx
Review Drill/Due Today
• A ball is thrown horizontally at 20 m/s.
How far does the ball travel in 0.639 s?
Solution
s
m20vix
0t i s639.0t
s
m20vfx
0a x
)0,0(
m78.12s639.0s
m20x f
0x i ?x f
A ball is thrown horizontally at 20 m/s. How far does the ball travel in 0.639 s?
Projectile Motion
Projectile Motion
Projectile Motion
Projectile motion is the combination of the linear motion in the x and
y directions.
Group Drill• Projectile gun. An enemy ship is observed 50
m off the coast. You plan to roll a large
bolder off of a horizontal cliff, 80 m above
the ocean. How fast must the bolder be
traveling in order to hit the enemy ship?
(Visualization, Reasoning, and Assess for
credit).
Trigonometry Review
r
ysin
r
xcos
x
ytan
r
x
y
222 ryx
Projectile Drill/Due Today
• A daredevil cyclists travels horizontally
off of a cliff at 50 m/s. If the ramp is
placed 30 m below the cliff, then how far
in the x-direction should a ramp be
placed, and at what angle should the ramp
be set at?
Projectile Drill/Solution
origin
?
0,
s
m50vi
m30,0
fyf v,
s
m50v
0,x f
ts
m50x f
mts
m309.40 2
2
ts
m8.9v
2yf
s/m50
vtan
fy
Long Jump Drill/Due Today• Mike Powell currently holds the long
jump record at 8.99 m. The average
person can run 50 m in 7.0 s. From what
height platform must an average person
run off of to land 9.00 m away?
Projectile Drill/Due Today