Download Physics 130 - University of North Dakota

9/11 Free Fall, Projectile Motion
Today:
examples
one new equation
HW “9/11 Stunt Man” Due Friday, 9/13
On web or in 213 Witmer for copying
Last years practice exam on web and in 213
Example 9 page 41 in text
From rest a motorcycle accelerates at 2.6m/s/s for a distance of
120m. How long did it take? How fast is it going?
Text uses vi2 = vf2 + 2ax
but fails to say how we multiply vectors.
This equation is off limits for us for this and other reasons but I
will give you one to use in these cases.
Combine v/ t = a and x/ t = vave with either vi or vf = 0…...
Get: t =
2 x
a
Now you can work out t, v,
and vf.
Example:
An object has an initial velocity of 20m/s directed at 53
above the horizontal. The acceleration is 4m/s2 directed
down. What is the object’s velocity 8s later?
vy = ?
v = 20m/s
16m/s up   = 53° above horizontal
vx = ? 12m/s right
ax = 0 so vx at 8s = 12m/s right
ay = 4m/s2 down so vy at 8s = 16m/s down

vy = 16m/s
down
vx = 12m/s right
 = 53° below horizontal
v = 20m/s
At what time is it
moving exactly
horizontal? 4s
What is its speed
at this time?
12m/s
Example: another look
An object has an initial velocity of 20m/s directed at 53
above the horizontal. The acceleration is 4m/s2 directed
down. What is the object’s velocity 8s later?
Just like we
vy = ?
v = 20m/s
vi
do for 1D
16m/s up   = 53° above horizontal
motion
vx = ? 12m/s right
v
vf

vy = 16m/s
down
vx = 12m/s right
 = 53° below horizontal
v = 20m/s
vi + v = vf
Example: A closer look
An object has an initial velocity of 20m/s directed at 53
above the horizontal. The acceleration is 4m/s2 directed
down. What is the object’s velocity 8s later?
Just like we
do for 1D
vi
motion
v
v/s =
vf
The horizontal component of the
velocity never changes.
vi + v = vf
g is not the “accel. of gravity”
g is always a “field strength”, not an acceleration!
It tells us how much force (in Newtons) is on an object
and depends on the object’s mass. Weight = mass x g
W = mg
An object in free fall (or in projectile motion) has only
the weight force on it as nothing else is touching it.
g is not the “accel. of gravity”
Newton’s 2nd Law
It tells us how much acceleration an object has and
depends on the object’s mass as well as the net force on
the object. acceleration = force (Weight)  mass
a = W/m = mg/m = g
a = g in number, not in concept!
2nd law W = mg (this is NOT the 2nd law)
Be careful: g = 9.8N/kg and for free fall a = 9.8m/s2 but
it is dangerous to think of g as an acceleration. More on
this later.
Projectile Motion Example:
An object is thrown with a velocity of 4m/s up and 3m/s
west. The acceleration is 10m/s2 directed down.
How long is the object in the air?
How high does it get?
What is its velocity when it gets back to the ground? (Well,
impact speed, not at rest.)
Find the Displacement
v
(m/s)
10
At what time is the object
back where it started from?
-8m/s What is its velocity at this
time?
10s
If it returns to its starting
10
t (s) point it must turn around.
At what time does it do
6s
that?
-10
What is the displacement
from 2s to 13s?
How many meters were put on the odometer from 2s to
13s?