•cover the section on, “motion in two or three dimensions.” skip “motion...

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