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A projectile is any object that is moving upwards
or downwards under the influence of gravity.
Examples of projectiles moving up or down:
1. Golf ball
2. Cricket ball
3. Bullet
4. Rocket (with engines off)
5. Stone thrown from top of a building
Which hits first?
Golf ball trajectories
What happens during the motion of a
ball that is thrown vertically upwards
into the air?
Vertical projectile motion
Describe the motion -
• The object starts with maximum velocity as it leaves the throwers hand
• The object slows down as it rises in the air
• The object momentarily stops at the top
• The object speeds up as it descends
• The final velocity of the object when it again reaches the throwers hand is the same as when it left the throwers hand
• At all times the object accelerates downwards due to the force of gravity.
Medicine ball - be sure to get out of the path!
Time for the
downward
journey = t
Time for the
upward
journey = t
a = g = 10
m/s2 down
a = g = 10
m/s2 down
vf = 0
vi = maximum
value up
vf = maximum
value down
vi = 0
Projectile motion click here
Objects falling with
horizontal forces
Falling water droplets
ACCELERATION
• At any point during the journey the acceleration of the object is equal to the gravitational acceleration, g.
• g = 10m/s2 down towards the earth.
• g is independent of the mass of the object.
• g is dependent upon the distance from the centre of the earth
Horizontal & vertical motion
Use equations of motion for a
projectile
vf = vi + g∆t
Δx = vit + ½ g∆t2
vf2 = vi
2 + 2gs
Δx = (vf + vi).∆t
2
Firing a cannon ball
Changing horizontal components
t
s/m
GRAPHS of MOTION for
PROJECTILE MOTION. Take up as +
t g/m/s2
t
s/m
t v/m/s
Gradient of the
graph = - 10m/s2
a = g= -10m/s2
(down).
Disp./time Velocity/time
Acceleration/time
Distance/time
These are known as ‘sketch graphs’ – since they have
no values on the respective axes.
Graphs of motion
Projectile motion
FREE FALL and TERMINAL VELOCITY
• Objects only accelerate downwards at 10
m/s2 (or 9,8m/s2) in a vacuum near earths
surface.
• In air, air resistance increases and decreases
acceleration to values less than 10 m/s2.
• Smooth objects experience less air
resistance and a = g initially for all objects.
• If air resistance is large and increasing,
acceleration decreases to zero and the object
falls at constant velocity, called terminal
velocity Falling raindrop Terminal velocity
Graph for acceleration and using a parachute
When the parachutist jumps,
her acceleration is 10 m/s2
downwards. The only force acting
on her is the force of the earth.
Fres is downwards
As her velocity increases, so does
the force of air resistance opposing
the downward force of gravity.
Fres is still downwards, but smaller.
Reaching terminal velocity
Air resistance is due to collisions with
the particles of air.
The greater the velocity of the parachutist, the
greater the number of collisions and the greater
the air resistance.
Fres decreases until it equals zero and a = 0.
The parachutist now
falls with a constant
velocity – called
terminal velocity
Terminal velocity Click here
What are you expected to do?
• Apply equations of motion to vertical
motion.
• Use graphs of motion to describe vertical
motion.
• Explain why some objects reach terminal
velocity when falling in the gravitational
field.
Tips to help you use the equations
of motion for projectile motion:
• Choose a direction as positive.
• Decide on the time interval that is relevant to the question.
• Write down known values - vi, vf, a, ∆x and t.
• If an object is released or dropped by a person that is moving up or down at a certain velocity, the initial velocity of the object equals the velocity of that person.
Apply your knowledge!!! A bullet is fired vertically upwards at 200m/s.
Ignore the effects of air resistance, and
calculate:
a. the maximum height reached.
b. the time taken for the bullet to be at a
height of 1500m on its way down.
c. at what height it will be moving
at 100m/s upwards.
This is how your answer should look:
a. Let up be positive for all answers
vi = +200 m/s
vf = 0 m/s
g = -10 m/s2
∆x = ?
vf2 = vi
2 + 2g∆x
0 = (200)2 + 2(-10) ∆x
∆x = + 2000m or 2000m up
b. Consider the time period from when the bullet was fired until it is 500m above the starting position.
vi = +200m/s g = -10m/s2
∆x = +500m t = ?
∆x = vit + ½ gt2
+500 = (+200)t + ½ (-10)t2
t = 10s or 30s
30s is when the bullet is on the way down.
c. Consider the time interval from when the bullet is fired until it has a velocity of 100m/s upwards
vi = +200m/s
vf = +100m/s
g = -10m/s2
vf 2 = vi
2 + 2g ∆x
(+100)2 = (+200)2 + 2(-10)s
s = 1500m
The acceleration due to gravity is 9.8 m.s-2.
It can differ from point to point on the earths surface – depending on the distance from the centre of the earth. All objects fall at this rate – irrespective of their mass.
However, we usually take it (g) as 10 m.s-2.
Discuss how the acceleration due to gravity could be determined by using a ticker tape and ticker timer.
g on different objects Coin & feather experiemnt
Position of object
Time/s Displacement/m Velocity/m.s-1 Acc. Due to gravity/m.s-2
0 0 0 10
1 5 10 10
2 20 20 10
3 45 30 10
4 80 40 10
Calculate the acceleration due to gravity from these values
g by free fall experiment
How can the value of g be determined by using the set up above and the equation ∆x = vit + 1/2 g t2 ?
Pendulum method
Alternate g by
pendulum method
Since the pendulum starts from rest, vi = 0 m.s-1
∆x = 1/2 g t2
The pendulum falls about 84 cm. in the time the metre rule falls through ¼ of a swing.
Take the time for 20 swings of the pendulum and then divide by 80 to find the time for ¼ of a swing.
Substitute into equation and solve for g.
Calculating g
In a vacuum all objects, irrespective of mass, shape or size, fall at the same rate of 9.8m.s-2
In reality, ‘g’ varies from point to point on the earth’s surface. This depends upon:
1. The change in radius from point to point.
2. The varying density of the earth’s surface from point to point.
At the poles ‘g’ is greater and less at the equator. Projectile Motion Click here Newtonian Mountain
Cannon ball into space
Shooting cannon ball
Feather & coin
experiment in vacuum