Transcript projectile powerpoint

Projectile Motion
AIM: how do we solve projectile problems in 2 dimensions?
DO NOW
1. What do you notice
about the horizontal
spacing of the dots?
2. What does this mean
about the horizontal
motion of a projectile?
3. What formula(s) can you
use?
Projectile Motion
• Horizontal Motion
–
–
–
–
Use the subscript x to denote horizontal numbers
Equally spaced lines implies constant speed
NO horizontal acceleration
Variables used
• vx
• dx
• t
– Formulas
•
d x  vxt
ax
vx
dx
t
t
t
Projectile Motion
AIM: how do we solve projectile problems in 2 dimensions?
1. What do you notice
about the vertical
spacing of the dots?
2. What does this mean
about the vertical
motion of a projectile?
3. What formula(s) can
you use?
• Vertical Motion
Projectile Motion
– Use the subscript y to denote vertical numbers
– Lines that get progressively farther apart imply vertical acceleration
– Variables used
•
•
•
•
•
viy
dy
ay
vfy
t
d x  vxt
v f  vi  at
– Formulas d  v t  1 at 2
i
•
vf
2
2
2
 vi  2ad
ay
vy
dy
t
t
t
Projectile Rules
1. Vertical acceleration is always 9.81m/s2
downwards for all objects at all times.
2. Horizontal acceleration is always zero.
3. You CAN NOT but a horizontal number in
the same equation as a vertical number.
4. “thrown horizontally” means…
- Viy is zero
- “Dropped” means Viy is zero
Projectile Rules
5. An object dropped and launched
horizontally from the same height will hit
the floor at the same time.
- Mass does not matter
- Horizontal launch speed does not matter
6. Final velocity is NOT zero
7. Time is the only number that has no
direction and can be used in any
equation.
How to solve a projectile
problem
1. Draw and label a diagram with every
number they give you.
2. Make a list of all horizontal and vertical
variables. KEEP THESE LISTS
SEPARATE!
3. If you do not have time, find it!
4. Using the time found/given solve for the
variable in question.
Step 1: Draw and label diagram
“launched
horizontally”
vx
trajectory
“height”
dy
dx
“Range” or
“distance from the
base”
Step 2: Separate variables
We separate them because we cant mix them in equations!!!!
Variable Chart
Horizontal Motion
(left and right)
constant speed
motion!
Vertical Motion
(up and down)
constant
acceleration!
viy =
ay =
dy =
t=
vfy =
vx =
dx =
t=
v f  vi  at
d=vt
1 2
at
2
2
 vi  2ad
d  vi t 
vf
2
Step 3: Solve for the variables asked for
• REMEMBER:
– you can not mix horizontal and vertical variables!
– only time is the same in both columns
– there is no vi horizontally because the horizontal
velocity is constant
– There is also NO horizontal acceleration
– The time of flight only depends on the vertical
variables Bullet dropped vs. bullet fired
• max time of flight is when an object is launched straight
up!
– maximum range is when an object is launched at
45o to the horizontal.
1. A toy car moving at 3m/s drives horizontally off of a 1.5m high table.
a. How long is the car in the air for?
b. How far away from the base of the table does the car land?
2. A set of keys is thrown horizontally at 12m/s from a window that is 30m high
a.How long are the keys in the air?
b.How far away from the base of the building do the keys hit the floor?
c.What is the final vertical velocity of the keys?
d.What is the final horizontal velocity of the keys? EXPLAIN!
3. A movie requires a car to drive horizontally off of a 50m high building. If the
stunt crew decides to place the airbag 15m from the base of the building
A. How fast should the car drive off the building?
B. What would happen if the car drove off slower?
C. What would happen if the car drove off faster?
D. What would happen if the movie director decided he wanted to use a
truck instead of a car? Would the stunt crew have to change the
location of the air bag or tell the truck to drive at a different speed?
DEFEND YOUR ANSWER!
4. A motorcycle drives horizontally off of a cliff that is 25m high
and is found 85m from the base of the cliff. If the speed limit
on the road is 35m/s, was the motorcycle speeding? (assume
the motorcycle didn’t skid after landing)
5. A rifle is shot perfectly horizontally and the bullet leaves the
barrel of the gun at 100m/s.
a. If the bullet is found 1.2km away from the gun, how high
was the gun mounted off the ground?
b. If the muzzle of the gun is 20cm long, what is the
acceleration of the bullet while in the muzzle of the
gun?
c. How long is the bullet in the gun for?
d. How long is the bullet in the air for?
6. You take a running start and jump horizontally off the roof of
your house that is 12m high in an attempt to land on the roof of
the building next door that is 7m tall. The horizontal spacing
between the buildings is 6m. If you can run at 6.2m/s, do you
make it?
Projectiles Launched at an Angle on
Level Ground
vi
θ
Step 1: Create Diagram
dmax
θ
dx “range”
Step 2: Break down angled
vector
θ
vx
viy
vx= vicosθ
viy= visinθ
Step 4: Decide which part of
motion you are looking at
Half Motion
TO the Top
• vi = ______
• vf=0m/s
• a=-9.81m/s2
• dmax=
• tup =
FROM the Top
• vi = 0m/s
• vf=______
• a=-9.81m/s2
• dmax=
• tdown =
Whole Motion
OR
•
•
•
•
•
vi = _______
vf= ______ (will be negative of v )
a=-9.81m/s2
dy =0m
ttotal = _____ (will be 2t =2t )
i
up
down
Step 3: Separate variables into
horizontal and vertical then solve
Horizontal Motion
(left and right)
constant speed motion!
Vertical Motion
(up and down)
constant acceleration!
viy =
ay =
dy =
t=
vfy =
vx =
dx =
t=
v f  vi  at
d=vt
1 2
d  vi t  at
2
2
2
v f  vi  2ad
4. A motorcycle moving at 35m/s drives off a ramp that makes an
angle of 50o to the horizontal. If the motorcycle lands at the
same height it jumped from
- What is the motorcycle’s mat height?
- How long is the motorcycle in the air for?
- How far away from the jump point does the motorcycle
land?
5. During a soccer game, the goalie kicks a goal kick at 28m/s at
an angle of 50o above the horizontal. How far from the goalie
does the ball land?
6. During a football game, the kicker attempts a field goal that is
50m from the goal post which are 4m above the ground. The
kicker kicks the ball at 22m/s at an angle of 42o above the
horizontal. Assuming he aims on target, is the field goal good?
If not why?
Projectiles Launched up and over
vi
θ
To the top
vi
θ
vf=0
From the top
dup
dmax
dy
TO the Top
• vi = ______
• vf=0m/s
• a=-9.81m/s2
• dup=
• tup =
FROM the Top
• vi = 0m/s
• vf=______
• a=-9.81m/s2
• dmax= dup+dy
• tdown =
Whole Motion
•
•
•
•
•
vi
θ
-dy
viy = vi sin θ
vfy=
ay =-9.81m/s2
d= -dy
ttotal =
make sure dy is negative
You can find vf first then plug it in (as a negative number) to find t
OR
Plug into the distance formula and use the quadratic equation to
get time.
6. You take a running start and jump off the roof of your house
that is 12m above the ground. You can run at a speed of 5m/s
and jump at an angle of 60o to the horizontal.
a. How long are you in the air for?
b. How far from the base of the house do you land?
7. A set of keys is thrown at 12m/s 35o above the horizontal from
a window that is 30m high
a. How long are the keys in the air?
b. How far away from the base of the building do the keys hit
the floor?
c. What is the final vertical velocity of the keys?
d. What is the final horizontal velocity of the keys? EXPLAIN!