Download Projectile Motion

PPMF101 – Lecture 4
Motions in 1 & 2 Dimensions
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Vector & Scalar quantity
Vector
A quantity that has
magnitude and
direction.
Scalar
A quantity that has
magnitude only.
Eg. Displacement,
velocity, acceleration,
force, momentum,
impulse, weight,
friction, tension,
electric and magnetic
field.
Eg. Distance, speed,
pressure, energy,
heat, work, power,
time, charge and
temperature.
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Distance & Displacement
Distance
Scalar quantity
Magnitude only
Displacement
Vector quantity
Magnitude and
direction
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Speed
Speed refers to how far an object
travels in a given time interval,
regardless of direction.
A scalar quantity.
total dis tan ce
average speed 
total time
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velocity
Velocity is used to signify both the
magnitude (numerical value) of how
fast an object is moving and the
direction in which it is moving.
A vector quantity.
total displacement
average velocity 
total time
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Instantaneous velocity
Instanteneous
velocity at any
moment is
defined as the
average velocity
over an
infinitesimally
short time
interval.
x
v  lim
t  0 t
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Acceleration
Acceleration specifies how rapidly the
velocity of an object is changing.
If velocity is increasing it is called
acceleration.
If velocity is decreasing it is called
negative acceleration or deceleration.
change of velocity
average acceleration 
time elapsed
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Instantaneous acceleration
v dv
a  lim

t  0  t
dt
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Graph: displacement (s) vs time (t)
Slope = velocity
s
s
t
t
constant
velocity
zero velocity
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Graph: displacement (s) vs time (t)
s
s
t
t
increasing
velocity
decreasing
velocity
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Graph: velocity(v) vs time(t) (p.25)
Slope = acceleration
Area under the graph
= distance travelled
v
v
t
t
constant velocity &
zero acceleration
velocity increasing
uniformly & constant
acceleration
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Graph: acceleration(a) vs time(t)
For constant
acceleration.
The graph is a
straight horizontal
line.
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v vs t & s vs t graphs: braking
distances
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S vs t & v vs t graphs: catching a
speeder (p.31)
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Equations of motion
Constant
acceleration a
v  u  at
1 2
s  ut  at
2
2
2
v  u  2as
1
s  u  v t
2
Constant
acceleration due to
gravity g
v  u  gt
1 2
s  ut  gt
2
2
2
v  u  2 gs
1
s  u  v t
2
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Examples
1. A runner leaves the starting blocks
and accelerates at 2.50 m/s2 for
4.00 s. What speed does the runner
reach?
2. An airplane that is flying level needs
to accelerate from a speed of 200
m/s to a speed of 240 m/s while it
flies a distance of 1200 m. What
must the acceleration of the plane
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be?
3. A rock is dropped from a vertical
cliff. The rock takes 7.00 s to reach
the ground below the cliff. What is
the height of the cliff?
4. If an object was freely falling, from
what height would it need to be
dropped to reach a speed of 70.0
m/s before reaching the ground?
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Eg. 1
Determine the average velocity for
(i) the first 3 seconds
(ii) the entire motion
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Eg. 2
This is a graph for a moving object.
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Eg. 2 continue
(i) Explain the motion at PQ and RS.
(ii) What is the total displacement of
the object?
(iii) What is the time for the motion
of the object?
(iv) Determine its average velocity.
(v) What is its acceleration at
t = 22 s?
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Eg. 3
A car is driven from point O at the
north with velocity 60 km/h for 10 min
until it reached a junction, S. The car
then turn west and moved with a
velocity of 30 km/h for another 10 min
until its reached point A. Determine
(a) the average speed of the car from
O to A.
(b) the average velocity of the car from
O to A.
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Eg. 4
A mouse deer runs a distance of 70 m
between two points at a constant
acceleration in 7.0 s. Its velocity while
passing through the second point is 15.0
m/s.
(a) What is its speed at the first point?
(b) What is the acceleration of the mouse
deer?
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Projectile Motion
A projectile is an
object moving in
two dimensions
under the
influence of
Earth's gravity; its
path is a parabola.
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Projectile Motion
If an object is launched at an initial angle of θ0 with
the horizontal, the analysis is similar if θ0 = 0
launched from certain height, except that the initial
velocity has a vertical component.
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Projectile Motion
It can be understood by
analyzing the horizontal
and vertical motions
separately.
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Projectile Motion
The speed in the x-direction is
constant; in the y-direction the
object moves with constant
acceleration g.
This photograph shows two
balls that start to fall at the
same time. The one on the
right has an initial speed in the
x-direction. It can be seen that
vertical positions of the two
balls are identical at identical
times, while the horizontal
position of the yellow ball
increases linearly.
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Projectile Motion
Projectile motion is motion with
constant acceleration in two
dimensions, where the acceleration
is g and is downward.
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Solving Problems Involving
Projectile Motion
Example 3-6: Driving off a cliff.
A movie stunt driver on a
motorcycle speeds horizontally
off a 50.0-m-high cliff. How fast
must the motorcycle leave the
cliff top to land on level ground
below, 90.0 m from the base of
the cliff where the cameras are?
Ignore air resistance.
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Projectile Motion
metal
grinding
Examples of projectile
motion. Notice the
effects of air
resistance.
Water fountain
fireworks
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