2011 projectile motion
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Transcript 2011 projectile motion
Once
a difficult problem for
cannoneers
If
the vertical and horizontal
components are separated, the
problem becomes simple.
Horizontal
– simple as a
ball rolling across the table
Use equations like x = v x t
Vertical
– simple as a free
falling gravity problem
Use equations ∆y = vi t +
(1/2)gt2
and vf = vi + gt
NOTE:
Air and other resistance is
being ignored for the time
being.
Consider
these diagrams to answer the
following questions:
a. Which shows the initial velocity?
a
b. Which shows the acceleration vector?
b
What determines the time for the cannon ball to hit the ground?
The
time for the cannon ball to hit the
ground is determined by the height from
which it drops.
Supposing a snowmobile is equipped with a
flare launcher which is capable of launching a
sphere vertically (relative to the snowmobile).
If the snowmobile is in motion and launches the
flare and maintains a constant horizontal
velocity after the launch, then where will the
flare land (neglect air resistance)?
a. in front of the snowmobile
b. behind the snowmobile
c. in the snowmobile
C
The
flare will land inside the snowmobile.
The flare has the same horizontal velocity
as the snowmobile that it was initially in.
The velocity does not change
http://www.physicsclassroom.com/mme
dia/vectors/pap.html
Horizontal Motion Vertical Motion
Forces
(Present?- Yes or No) If
present, what direction
No
Yes
The force of gravity acts
downward
Acceleration
No
“g” is downward at -9.81 m/s2
(Present?- Yes or No)
If present, what direction?)
Velocity
(Constant or Changing)
Yes
Constant
Changing
(by -9.81 m/s each second)
How high is the table?
Time
of fall
vx = x/t
30 m/s = 120 m / t
t = 4.0 s
Height of table
∆y = vit + ½ gt2
∆y = ½ (-9.81 m/s2)(4.0s)2
∆y = -78 m………78m
At what speed will it hit the ground?
Horizontally
30
speed is constant.
m/s = vx
Vertical Speed
vf = vi + gt
vf = (-9.81 m/s2 )4.0 s
vf = 39 m/s
Resultant speed = 49 m/s
Planar
motion
Air resistance: negligible
Gravity: downward
No horizontal acceleration
Constant vertical acceleration
Parabolic trajectory
Independent horizontal and vertical
motions
Question 4
Anna Litical drops a ball from rest from the top of
80.-meter high cliff. How much time will it take for
the ball to reach the ground and at what height will
the ball drop after each second of motion?
∆y
= vit + ½ gt2
-80.m = ½ (-9.81 m/s2)t2
-160m = (-9.81 m/s2) t2
t = 4.0 s
Each sec the displacements are as
follows: ∆y = vit + ½ gt2 = ½ (9.81m/s2)(1sec)2
-4.9m, -20m,-44m,-78m
Question 5
A cannonball is launched horizontally from the top
of an 80.-meter high cliff. How much time will it take
for the ball to reach the ground and at what height
will the ball be after each second of travel?
∆y
= vit + ½ gt2
-80.m = ½ (-9.81 m/s2)t2
-160m = (-9.81 m/s2) t2
t = 4.0 s
Each sec the displacements are as
follows: ∆y = vit + ½ gt2 = ½ (9.81m/s2)(1sec)2
-4.9m, -20m,-44m,-78m
A
pool ball leaves a 0.60-meter high
table with an initial horizontal velocity
of
2.4 m/s. Predict the time required for
the pool ball to fall to the ground and
the horizontal distance between the
table's edge and the ball's landing
location.
Vertical Time
∆y
= vit + ½ gt2
-.60m = ½ (-9.81 m/s2)t2
-1.20m = (-9.81 m/s2) t2
t = .35 s
Horizontal Distance
x = v (t) = 2.4 m/s ( .3497s) = .84m
A
soccer ball is kicked horizontally off a
22.0-meter high hill and lands a distance
of 35.0 meters from the edge of the hill.
Determine the initial horizontal velocity
of the soccer ball.
Vertical Time
∆y
= vit + ½ gt2
-22m = ½ (-9.81 m/s2)t2
-44m = (-9.81 m/s2) t2
t = 2.1 s
Initial Horizontal Velocity
vx = x/t = 35 m/2.1178s = 17 m/s
You
accidentally throw your car keys
horizontally at 8.0 m/s from a cliff 64 m
high. How far from the base of the cliff
should you look for the keys?
A
toy car runs of the edge of a table that
is 1.225 m high. If the car lands 0.400 m
from the base of the table,
a. how long did it take the car to fall?
b. how
table?
fast was the car going on the
Divers
in Acapulco dive from a cliff that is
61 m high. If the rocks below the cliff
extend outward for 23 m, what is the
minimum horizontal velocity a diver must
have to clear the rocks?
A
dart player throws a dart horizontally at
a speed of 12.4 m/s. The dart hits the
board 0.32 m below the height from
which it was thrown. How far away is the
player from the board?
A
ball thrown horizontally from a 13 m
high building strikes the ground 5.0 m
from the building. With what velocity was
the ball thrown?
A
person leaps horizontally from the top
of a tower and lands 17.0 m from the base
of the tower. If the speed at which the
person was projected was 9.50 m/s, how
high is the tower?
Problem
Solving Approach
Carefully read the problem. List known and unknown
information
For convenience sake, make a table with horizontal
information on one side and vertical information on the other
side.
Identify the unknown quantity which the problem
requests you to solve for.
Select either a horizontal or vertical equation to
solve for the time of flight of the projectile.
With the time determined, use one of the other equations to
solve for the unknown. (Usually, if a horizontal equation is used to
solve for time, then a vertical equation can be used to solve for the
final unknown quantity.)
Velocity
Trajectory
Up to a 45 degree angle – greater
distance at greater angle
After 45 degree – greater height, less
distance
45 degree gives the greatest distance
Any two angles that add to 90 degrees
will hit the same place
Sky-diver in free fall
Abc
Terminal velocity is reached when f(v) = g