pptg101213 free fall & projectile notes gallego

Constant Acceleration |Freefall| Constant Velocity |Projectile

3 August 2012 1 REDG 2011

Motion with Constant Acceleration


A feather is dropped on the moon from a height of 1.40 meters. The feather accelerates to the ground at 1.67m/s2. Determine the time for the feather to fall to the surface of the moon.



A stone is dropped from the top of the building that is 100m tall. The stone accelerates to the ground at 10m/s2. Determine the time for the stone to fall to the ground.



t1= 10m/s

t2= 20m/s

t3= 30m/s

t4= 40m/s

t5= 50m/s

Time (s) Velocity (m/s) Distance (m)

0 0 0

1 10 5

2 20 20

3 30 45

4 40 80

5 50 125

d at 21

2



When an object is falling under the influence of gravity alone, it is undergoing a freefall.

t1= 10m/s

t2= 20m/s

t3= 30m/s

t4= 40m/s

t5= 50m/s



t1= 10m/s

t2= 20m/s

t3= 30m/s

t4= 40m/s

t5= 50m/s

When an object is falling under the influence of gravity alone, it is undergoing a freefall.

mdt

a

2 1002 m

10s

4.47s

2

Freefall & NOT Freefall


Tell whether each situation is undergoing freefall or not

Freefall & NOT Freefall


Which will hit the ground first?

Freefall

3 August 2012 10 REDG 2011

An object undergoing a freefall undergoes an

acceleration due to gravity, g, that is 9.8 m/s2

Freefall

3 August 2012 11 REDG 2011

If a freely falling rock were equipped with speedometer, by how much would its speed reading increase with each second of fall?

Freefall

3 August 2012 12 REDG 2011

When a ball is thrown straight up, by how much does the speed increase or decrease each second? (Neglect air

resistance)

Will its velocity reach zero while it is up in the air?

Freefall

3 August 2012 13 REDG 2011

Elephant Snail Feather

The elephant, snail and the bird planned to jump off from a plane high above the ground. Because the bird was

trapped in the cage, only its feather has escaped. Neglecting air resistance, which will hit the ground first?

Freefall

3 August 2012 14 REDG 2011

• If all jumped (feather dropped) from the plane, what it their initial velocity?

• If air resistance is ignored, which one has the greatest acceleration?

Freefall

3 August 2012 15 REDG 2011

• If they started from the same height, leaves with the same initial velocity, and subjected to the same acceleration, then, which will take longer time in air before hitting the ground?

Freefall

3 August 2012 16 REDG 2011

A stone is dropped from the top of the building that is 100m tall.

A stone is thrown downward from the top of the building that is 100m tall.

What is the difference between these two problems?

vi = 0 vi > 0

Freefall

3 August 2012 17 REDG 2011

A stone is dropped from the top of the building that is 100m tall.

A stone is thrown downward from the top of the building that is 100m tall.

What is the difference between these two problems?

Acceleration due to gravity

Freefall

3 August 2012 18 REDG 2011

Freefall

3 August 2012 19 REDG 2011

A coin is dropped in a vacuum tube, find its displacement after 0.30 seconds.

Identify the given, unknown and the equation of the unknown. Further, solve the equation.

t = 0.30s vi = 0 g = 9.8m/s2

d =?

Freefall

3 August 2012 20 REDG 2011

An egg was thrown straight down from top of a building at a speed of 15m/s. It hit the ground 2.75s later. At what speed did it hit the ground?


t = 2.75s vi = 15m/s g = 9.8m/s2

vf =?

Freefall

3 August 2012 21 REDG 2011

An egg was thrown straight down from top of a building at a speed of 15m/s. It hit the ground 2.75s later. How high from the ground was the egg before it was thrown?


t = 2.75s vi = 15m/s g = 9.8m/s2

d =?

Freefall

3 August 2012 22 REDG 2011

A cannon ball is fired straight up from the ground and returned 12.0s later. What is the velocity of the cannon ball when it was fired?


t = 12.0s vi = ? g = -9.8m/s2

vf =0

Freefall

3 August 2012 23 REDG 2011

A kangaroo is capable of jumping to a height of 2.62 m. Determine the takeoff speed of the kangaroo.


2.62m

Freefall

3 August 2012 24 REDG 2011

If a rock from rest, equipped with speedometer, is freely falling what would the speedometer reading be 4.5s after it is dropped? How about 8 seconds after it is dropped? 15 seconds?


t=0

t=1

t=4.5?

t=8? t=15?

When something is undergoing freefall its velocity increases by 9.8m/s in every second of its descent. However, there comes a time that velocity no longer increase, thus no longer accelerates. In this case, the falling something reaches its terminal velocity.

Terminal Velocity

3 August 2012 25 REDG 2011

Terminal Velocity

3 August 2012 26 REDG 2011

Terminal Velocity

3 August 2012 27 REDG 2011

Does a raindrop reach terminal velocity? What if the raindrops do not reach terminal

velocity? What is the acceleration of a falling object

that reaches terminal velocity?

Terminal Velocity

3 August 2012 28 REDG 2011

If rain drops do not reach terminal velocity….

Reaction Time

3 August 2012 29 REDG 2011

Reaction Time

3 August 2012 30 REDG 2011

Reaction time is the interval time between the presentation of a stimulus and the initiation of the muscular response to that stimulus.

Reaction Time

3 August 2012 31 REDG 2011

Determine your reaction time

Trial Initial reading

Final reading

Difference

1

2

3

Average

*Convert all units in meters

dt

g

2

Reaction Time

3 August 2012 32 REDG 2011

What does a longer reaction time imply?

Projectile Motion

3 August 2012 33 REDG 2011

Mr. Suave had his rifle shooting session. He noticed that when he fired the rifle horizontally, the shell of the bullet drops from the rifle directly to the ground. Which will hit the ground first, the head or the shell of the bullet? Explain.

Projectile Motion

3 August 2012 34 REDG 2011

Without the influence of the gravity, a canon ball that is fired horizontally will travel at constant velocity. Thus, equal distance covered in every equal time interval.

Projectile Motion

3 August 2012 35 REDG 2011

Without being fired horizontally, a canon ball will drop undergoing a free fall. Thus, as it is falling, it accelerates at 9.8m/s2.

Projectile Motion

3 August 2012 36 REDG 2011

Under real condition, a canon that is fired horizontally will have constant horizontal velocity. However, it is also acted upon by the gravity thus, as it is travelling horizontally, in also travelling vertically at the acceleration due to gravity, 9.8m/s2.

Projectile Motion

3 August 2012 37 REDG 2011

Horizontal motion = non accelerating Vertical motion = freefall

Projectile Motion

3 August 2012 38 REDG 2011

Projectile Motion

3 August 2012 39 REDG 2011

Mr. Suave had his rifle shooting session. He noticed that when he fired the rifle horizontally, the shell of the bullet drops from the rifle directly to the ground. Which will hit the ground first, the head or the shell of the bullet? Explain.

3 August 2012 REDG 2011 40

Projectile Motion

3 August 2012 41 REDG 2011

A heavy crate accidentally falls from a high-flying airplane just as it is directly above a shiny red BMW smartly parked in a car lot. Relative to the BMW, where will the crate crash?

3 August 2012 REDG 2011 42

3 August 2012 REDG 2011 43

When the stealth bomber moves at a

certain velocity, all that are inside it are moving with the same velocity.

When a bomb is released by the stealth bomber, the bomb will undergo

freefall.

Even if the bomb is falling, it continues of

moving horizontally with the same velocity as the

stealth bomber.

3 August 2012 REDG 2011 44

3 August 2012 REDG 2011 45

Projectile Motion

3 August 2012 46 REDG 2011

A projectile is launched at an angle into the air. Neglecting air resistance, what is its vertical acceleration? Its horizontal acceleration?

Projectile Motion

3 August 2012 47 REDG 2011

Without the influence of the gravity, a canon ball that is fired horizontally will travel at constant velocity. Thus, equal distance covered in every equal time interval.

d vt

Projectile Motion

3 August 2012 48 REDG 2011

Without being fired horizontally, a canon ball will drop undergoing a free fall. Thus, as it is falling, it accelerates at 9.8m/s2.

Projectile Motion

3 August 2012 49 REDG 2011

The boy on a tower that is 5m high throws a ball to a distance of 20m. At what speed is the ball thrown?

5m

20m

Projectile Motion

3 August 2012 50 REDG 2011

The boy on a tower that is 10m high throws a ball to a distance of 20m. At what speed is the ball thrown?

10m

20m

Projectile Motion

3 August 2012 51 REDG 2011

A battleship (disguising pirate) simultaneously fires two shells at pirates aboard stolen ships. If the shells follow the trajectories shown below, which ship gets hit first?

A B

Projectile Motion

3 August 2012 52 REDG 2011

Which shell stays in the air for longer time?

A B

Hang Time

3 August 2012 53 REDG 2011

The hang time of an object is the length of time that it is aloft after leaving the ground.

Hang Time

3 August 2012 54 REDG 2011

The hang time of Michael Jordan is the length of time that he stays in the air, still, under the influence of the gravity.

Hang time = time going up + time going down

Hang Time

3 August 2012 55 REDG 2011

The hang time of the dolphin is the length of time that it stays in the air, still, under the influence of the gravity.

Hang Time

3 August 2012 56 REDG 2011

The hang time of the dog is the length of time that it stays in the air, still, under the influence of the gravity.

Hang Time

3 August 2012 57 REDG 2011

When you jump upward, your hang time is the time your feet are off the ground. Which has a longer hang time, the one who jumps 0.2 meters upward or the one who jumps the same height but an angle with the ground?

0.2m

Hang Time

3 August 2012 58 REDG 2011

If a kangaroo is capable of jumping to a height of 2.62 m. Determine its hang time.

Identify the given, unknown and the equation of the unknown.

2.62m 2dt=

g

2(2.62)t'=2t 2 2 0.73 1.46

9.8 s

Solution:

Given: d=2.62m; g=9.8m/s2; t’=2t=?

Hang Time

3 August 2012 59 REDG 2011

If Michael Jordan has a vertical leap of 1.29 m, then what his hang time?

Identify the given, unknown and the equation of the unknown.

1.29m 2dt=

g

2(1.29)t'=2t 2 2 0.263 0.53

9.8 s

Solution:

Given: d=2.62m; g=9.8m/s2; t’=2t=?

Problems on Projectile

3 August 2012 60 REDG 2011

Two golfers each hit the ball at the same speed but one at 60o with the horizontal and the other is at 30o. Which ball goes farther? Which hits the ground first?


3 August 2012 61 REDG 2011

Since the Moon is gravitationally attracted to the Earth, why doesn’t it simply crash into the Earth?

Identify the given, unknown and the equation of the unknown. Finally, solve the problem.


3 August 2012 62 REDG 2011


2d 2(1.3)t= 0.52

g 9.8

d=v t = 4.0 0.52 = 2.1m

y

x

s

Solution:

Given: dy=1.3m dx=? g=9.8m/s2

vx= 4.0m/s


3 August 2012 63 REDG 2011


2d 2(100)t= 4.52

g 9.8

d 20 mv = = = 4.42

t 4.52 s

y

xx

s

Given: dy=100m dx=20 g=9.8m/s2

vx= ?


3 August 2012 64 REDG 2011


2d 2(19.3)t= 1.98

g 9.8

d 26.3 mv = = = 13.28

t 1.98 s

y

xx

s

Given: dy=19.3m dx=26.3m g=9.8m/s2

vx= ?


3 August 2012 65 REDG 2011

2

iyv = accelerated (-9.8m/s )

ixv = constant speed

iv


3 August 2012 66 REDG 2011

iy iv =v sinθ

ix iv =v cosθ

iv


3 August 2012 67 REDG 2011

iyv 0

fyv 0

iy iv = v sinθ

fy iy

fy iy

iy

iy

v -vg=

t

v -vt=

g

0-vt=

g

vt=

g

iv sinθt =

g

iy

hang time, t'=2t

2vt'=

g

i2v sinθt' =

gtup tdown

t = tup down


3 August 2012 68 REDG 2011

iyv 0

fyv 0ix iv = v cosθ

x ix

x i

R or d =v t'

R or d =v cosθ t'


3 August 2012 69 REDG 2011


Given: = 30o

vi= 6m/s R=?

i

2

2

i

ii

x

2v sinθt' =

g

2v sin

2v cosθsinθ

g

θR

R or d =v cosθ t'

v c

2(6) cos30

o=g

sin30

9.8

3.1

sθ

8

i

m


3 August 2012 70 REDG 2011

At which point in its trajectory does a batted baseball have its minimum speed?


3 August 2012 71 REDG 2011

A projectile is fired upward at the speed of 141m/s, 45o to the horizontal. What is its velocity when it reached the top of its trajectory?


When the projectile reach the topmost of its trajectory, the velocity along y or vfy=0 but vx is not equal to zero.


3 August 2012 72 REDG 2011

A cannonball shot with an initial velocity of 141m/s at an angle 45o follows a parabolic path and hits the balloon at the top of its trajectory. Neglecting air resistance, how fast is the cannon ball going when it hits the balloon?


Given: = 45o

vi= 141m/s g= 9.8m/s2

vx=?

i

m

s

v = v cosθ

141 cos45

99.7

x


3 August 2012 73 REDG 2011

Determine the range of a ball launched with a speed of 40m/s at angles (a) 40o

(b) 45o

(c) 50o

from the ground level


Problems on Projectile (Challenge)

3 August 2012 74 REDG 2011

Daring Phoebe wishes to cross the Grand Canyon of the Snake River from being shot from a cannon. She wishes to be launched at 60o with the horizontal so that she can spend more time waving to the crowd. With what speed must she be launched to cross the 520m canyon?


pptg101213 free fall & projectile notes gallego

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