2. Projectile motion consists of motion in 2-Projectile motion consists of motion in 2-
dimensions:dimensions: up-downup-down andand horizontalhorizontal motions.motions.
We will look at two types of projectile motion:We will look at two types of projectile motion:
1.1. Horizontal PMHorizontal PM. Initial velocity only has a. Initial velocity only has a
horizontal velocity component.horizontal velocity component.
2.2. Vertical PMVertical PM. Here, there is an initial vertical. Here, there is an initial vertical
velocity componentvelocity component
Of the two, horizontal PM is the easier to analyze.Of the two, horizontal PM is the easier to analyze.
How does the horizontal component affect the rateHow does the horizontal component affect the rate
at which the object falls? (see videos)at which the object falls? (see videos)
http://www.youtube.com/watch?v=z24_ihikEqQhttp://www.youtube.com/watch?v=z24_ihikEqQ (very brief)(very brief)
http://www.youtube.com/watch?v=qErh402eJgI&feature=relatedhttp://www.youtube.com/watch?v=qErh402eJgI&feature=related
3. From the videos, we can conclude that:From the videos, we can conclude that:
Horizontal velocity does not affect the rate atHorizontal velocity does not affect the rate at
which the object falls.which the object falls.
To analyze PM, we must:To analyze PM, we must:
1.1. Consider horizontal and vertical motionsConsider horizontal and vertical motions
separately.separately.
2.2. Ignore air resistance, which means that theIgnore air resistance, which means that the
horizontal velocity is ____________ .horizontal velocity is ____________ .
3.3. Let the vertical velocity component be affectedLet the vertical velocity component be affected
by only the force of gravity.by only the force of gravity.
4. The range is equal to:The range is equal to:
R =R = (2h/g)(2h/g) ½½
vv11
Where “vWhere “v11” is the initial” is the initial
horizontal velocityhorizontal velocity
Terms used:Terms used:
The path of the projectile is called__________ .The path of the projectile is called__________ .
The horizontal distance traveled (d) is called______The horizontal distance traveled (d) is called______
To determine the range, we must find the time of flight. We doTo determine the range, we must find the time of flight. We do
this by analyzing vertical motionthis by analyzing vertical motion..
h = vh = v1vertical1vertical Δt + 1/2(g)Δt + 1/2(g)((Δt)Δt)22
Δt = (2h/g)Δt = (2h/g) ½½
,, sincesince vv1vertical1vertical = 0.= 0.
U p
W E
T o p o f H ill
V 1
h
C a n n o n B a r r e l
d
N o t t o s c a le
W A T E R
V2
5. To determine the speedTo determine the speed
with which the projectilewith which the projectile
will have just before itwill have just before it
hits the water, we musthits the water, we must
add the horizontaladd the horizontal
velocity component andvelocity component and
the vertical component.the vertical component.
vv2vertical2vertical = v= v1vertical1vertical +g+gΔtΔt
vv2vertical2vertical = 0 +g= 0 +g (2h/g)(2h/g) ½½
vv2vertical2vertical = 0 += 0 + (2gh)(2gh) ½½
If vIf vHorizHoriz = 6.0m/s, h == 6.0m/s, h = 12.0 m12.0 m
, Then:, Then: Δt = 1.6 s, R = 9.4 m,Δt = 1.6 s, R = 9.4 m,
vv22 = 16.5 m/s [68= 16.5 m/s [6800
down fromdown from
horizontal]horizontal]
U p
H o r iz o n t a l
v H o r iz o n t a l
v2Vertical
=(2gh)1/2
v2
=
(v
2
Horiz.
+2gh)
1/2
