Projectile motion is motion
under the influence of gravity.
• object moves both
horizontally and vertically
Two-Dimensional Motion
Which hits the ground first, a bullet dropped straight down or one shot horizontally at a very high speed?
Misconception!!
- An object at rest will drop to the
ground faster than the same object moving horizontally at a high speed
Truth!!
- The horizontal motion of an object has no effect on the vertical motion.
- Gravity always acts downward, there is no “sidewaysness” to it.
Part 1 Projectiles Launched Horizontally
To hit a target across the room with a dart gun.
•Should we aim at, above, or below the target?
____________ above
Does a Projectile Accelerate??
YES!!! - a projectile does accelerate vertically since it is in freefall.
- Gravity is pulling it down at -10 m/s
2. NO!!! – a projectile does not accelerate
horizontally since there is nothing making it accelerate.
- A projectile moves at a constant velocity horizontally.
Yes and No
Calculating the Range – horizontal component
The range is the horizontal distance traveled by a projectile.
x
h= horizontal distance or range (m)
v
i= v
f= constant speed (m/s) a = acceleration = 0 m/s
2t = time (s)
A projectile travels at a constant velocity horizontally.
v
f= v
i+ at
x
h= v
it + ½at
2v
f2= v
i2+ 2ax
hCalculating Distance Fallen- vertical component
Same as free fall problems.
x
v= v
it + ½gt
2x
v= vertical distance or distance fallen (m) will be negative g = -10 m/s
2v
i= speed = 0 m/s
(if fired horizontally)t = time (s)
g t 2x
vIf projectile is fired horizontally, vi in the vertical sense is = 0
To find time, you can use
x
v= ½gt
2A bullet is fired horizontally at a speed of 50 m/s from a height of 3 meters. How
much time would it take the bullet to hit the ground?
t = _____ s If the bullet was fired at 100 m/s, how much time would it take to hit the ground?
t = ___ s 0.77
0.77
g t 2x
USE v
Horizontal Speed does not matter!
Monkey Joe throws a banana horizontally from a 45 m tall cliff at a speed of 25 m/s.
a) How much time does it take for the banana to hit the ground?
t = ___ s 3 b) What is the range of the banana?
x h = __ m
Use x
h= v
it + ½at
2g t 2x
USE
vBut Remember, there is no horizontal acceleration, so if a = 0 m/s
2- the equation changes to: x
h= v
it
75
x
v= 45 m
v
i= 25 m/s
A rock is thrown horizontally from a 50 meter tall building at 15 m/s.
t = _____ s (b) Now find the range. x h = ___ m
3.16 47.4
Vertical
x
v= -50 m
v
i= 0 m/s v
f= ?
a = -10 m/s
2t = ?
Horizontal
x
h= ?
v
i= 15 m/s v
f= 15 m/s a = 0 m/s
2t = ?
(a) How long a time has it traveled horizontally
before hitting the ground?
Vertical
x
v= v
i=
v
f= a = t =
0 m/s ? -10 m/s ?
24 s Horizontal
x
h=
v
i= v
f= a = t =
?
30 m/s 30 m/s 0 m/s
24 s
A cannon ball is shot horizontally at 30 m/s
from the top of a cliff, and it takes 4 seconds
for the ball to hit the ground.
a) How tall is the cliff?
x v = _______
b) What is the range of the cannon ball?
x h = ___ m
-80 m down
120 Vertical
x v = v i t + ½ gt 2
x v = (0 m/s)(4s) + ½(-10 m/s 2 )(4s) 2
x v = 0 m + (-80 m)
Horizontal
x h = v i t + ½ at 2
x h = (30 m/s)(4s) + ½(0 m/s 2 )(1s) 2
0
x h = 120 m + 0 m
0
1. A bridge is 176.4 m above a river. If a lead fishing weight is thrown from the
bridge with a horizontal speed of 22 m/s, a. How much time is it in the air?
b. what horizontal distance will it travel before striking the water?
Practice Questions
t = _____ s
x h = ____ m
5.94
130.7
2. Divers at Acapulco dive from a cliff that is 61.0 m high. If the rocks below the cliff extend outward for 23 m,
a) For how much time is the diver in the air?
b) What is the minimum initial speed a diver must have to clear the rocks below (i.e.
have a range of at least 23 m) ?
Practice Questions
t = _____ s 3.49
Use x h = v i t
Re-arrange v i = x h /t v
i= _____ m/s 6.59
3. Monkey Joe throws a banana horizontally from a height of 1.5 meters above the
ground. The banana lands 15 meters from where he threw it.
a) How long was the banana in the air?
b) What was the initial velocity of the banana?
t = _____ s 0.548 Practice Questions
27.37
v
i= _____ m/s
c) What was the velocity of the banana right before it hit the ground?
Looking for final velocity (v
f)
Have to determine both horizontal & vertical v
fcomponents and then add them together as vectors
To find vertical component use v
f2= v
i2+ 2gx
v Since vertical v
i= 0 m/s, v
f2= 2gx
v Therefore, vertical component of v
f= 5.48 m/s
Horizontal component of v
f= same as initial velocity
= 27.37 m/s
Use trigonometry to determine resultant v
f27.37 m/s
5.48 m/s 27.91 m/s
11.5o
Answer Final velocity is 27.91 m/s;
11.5
obelow the horizontal.
A woman drops an apple out of the window of a car moving at 18 m/s. If the car window is 1.0 m above the ground. How far horizontally will the apple travel before it hits the ground?
x
h= ___ m
Vertical
x
v= -1 m v
i= 0 m/s v
f= ?
g = -10 m/s
2t = ?
Horizontal
x
h= ?
v
i= 18 m/s v
f= 18 m/s a = 0 m/s
2t = ?
Practice Questions
g t 2x
vFirst find time using
t = ____s 0.447
0.447 s 0.447 s
Next, use x
h= v
it + ½at
2But Remember, there is no horizontal
acceleration, so if a = 0 m/s
2- the equation changes to: x
h= v
it = 18 x 0.447 = 8.05 m
8.05
A 100 g ball rolls off a table and lands 2 m
from the base of the table. A 200 g ball rolls off the same table with the same speed. It lands at distance:
a. <1 m.
b. 1 m.
c. between 1m and 2 m.
d. 2 m.
e. > 2 m.
A turtle running at 0.5 m/s and a rabbit
running at 5 m/s both run horizontally off of a small hill of height 2 meters. They both leave the cliff at the exact same moment.
a) Who hits the ground first?
b) How far apart are they after they both hit the ground?
a) Same time (0.632 s)
b) 2.844 m apart (3.160 m - 0.316 m)
Practice Questions
End of Part 1 – Horizontal Launch
Collect Data for “Punting Around” LAB
Continue with Part 2 – Launching at an Angle
horizontal component vertical component
resultant
Part 2 Projectiles Launched At An Angle
What is the shape of the motion of a projectile?
a) Linear (straight line) b) Circular
c) Parabola
You are sitting in the back seat of a convertible moving straight ahead holding a basketball in
your hands. You throw the basketball straight up, where will the ball land?
•In front of the car
•In the car
•Behind the car
A cannon ball is fired through the air.
What is the velocity at the top of its path?
Misconception: The velocity of the cannonball at the top of its path is 0 m/s
Truth: The horizontal velocity of a projectile does not change, so the ball has a horizontal velocity at the top equal to its initial horizontal velocity.
Vertical velocity is zero at the top.
1. A cannonball is fired at an angle of 30
oto the horizontal and with a velocity of 30 m/s.
a) How long a time is the ball in the air?
b) How far did it travel in the air?
2. Call up and to the right positive.
1. Draw a picture.
V
i= 3 0 m /s
= 30
oV
h= (30 m/s) cos 30
oV
h= 26 m/s
V
v= (30 m/s) sin 30
oV
v= 15 m/s
3. Find the vertical & horizontal components
of the initial velocity it was fired with.
Horizontal
x
h= v
i=
v
f= a = t =
Vertical
x
v= v
i=
v
f= a = t =
15 m/s ?
0 m/s at top - 10 m/s
2? 26 m/s ?
26 m/s 0 m/s
2?
a) Find Time: (only use vertical!!)
v f = v i + at
m/s 2
10 -
m/s 15
m/s
0
= 1.5 s
Therefore total time up & down = t
total= 3 s
30 m/s
