High School
by SSL Technologies
Physics Ex-32
Projectile motion is the vectorial sum of two independent velocities,
a horizontal component and a vertical component.
In solving problems on projectile
motion, work out the vertical and
The actual or instantaneous velocity at any point along the parabolic
component
velocities
path ishorizontal
tangent to the parabola
and equal to the
vectorial sum of the
horizontal and vertical component velocities.
separately as if they were
two separate problems.
The horizontal component velocity (VH) is constant throughout the
motion while the vertical component velocity (VV) equals free fall.
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Physics Ex-32
Question-1
Two stones, A and B, are used in an experiment. At the same time
that stone A is dropped, stone B is thrown down horizontally with
a velocity of 25 m/s. For each second of fall, fill in the velocities
of both stones, as indicated. (You need not include the units)
0
10
20
30
40
50
0
25
10
25
20
25
30
25
40
25
50
25
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Question-2
Physics Ex-32
A stone is dropped from a balcony 20 m high. How long does
it take the stone to reach the ground?
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Physics Ex-32
Question-3
A ball is thrown horizontally from a 20 m high cliff with
a velocity of 10 m/s. How far from the base of the cliff
does the ball land?
NOTE
The time it takes the ball
to strike the ground is the
same time it takes an
object to fall freely 20 m.
Step-1: Calculation of falling time
Step-2: Calculation of range
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Question-4
Physics Ex-32
A ball is thrown in the air with a velocity of 20 m/s at an angle
of 60o from the horizontal. Calculate:
a) How high it rises (the height).
NOTE
The vertical component of
the velocity is identical to
shooting an object
vertically upwards.
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Question-4
Physics Ex-32
A ball is thrown in the air with a velocity of 20 m/s at an angle
of 60o from the horizontal. Calculate:
b) How far it travels (the range).
NOTE
The horizontal component
of the velocity is the same
throughout the flight and is
thus an average velocity.
Multiply by 2 to obtain total time.
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Question-5
Physics Ex-32
A ball is thrown in the air with a velocity of 20 m/s at an angle
of 45o from the horizontal. Calculate:
a) How high it rises (the height).
NOTE
The vertical component of
the velocity is identical to
shooting an object
vertically upwards.
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Physics Ex-32
Question-5
A ball is thrown in the air with a velocity of 20 m/s at an angle
of 45o from the horizontal. Calculate:
b) How far it travels (the range).
NOTE
The horizontal component
of the velocity is the same
throughout the flight and is
thus an average velocity.
Multiply by 2 to obtain total time.
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Question-6
Physics Ex-32
A ball is thrown in the air with a velocity of 20 m/s at an angle
of 30o from the horizontal. Calculate:
a) How high it rises (the height).
NOTE
The vertical component of
the velocity is identical to
shooting an object
vertically upwards.
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Question-6
Physics Ex-32
A ball is thrown in the air with a velocity of 20 m/s at an angle
of 30o from the horizontal. Calculate:
b) How far it travels (the range).
NOTE
The horizontal component
of the velocity is the same
throughout the flight and is
thus an average velocity.
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Physics Ex-32
Question-7
The table below summarizes the answers from the previous three
questions (4, 5 and 6):
Initial velocity
Question-4
Angle
REMEMBER
60
20 m/s
o
Height
Range
15 m
35 m
20 m/s
45
m
40 m
The greatest
range
is10always
Question-6
20 m/s
30
5m
produced
by an angle
of 4535o.m
Question-5
o
o
a) Which angle produces the greatest height?
60o
b) Which angle produces the greatest range?
45o
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Question-8
Physics Ex-32
A cannon ball is fired into the air at an angle of 40o from the
horizontal and rises 5 m. Calculate its range.
Time = 1 s going up + 1 s coming down
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Question-9
Physics Ex-32
A ball is thrown into the air from a cliff 20 m high. If the ball is
thrown with a velocity of 15 m/s at an angle of 30o above the
horizontal, calculate how far from the base of the cliff the ball
hits the ground.
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Question-10
Physics Ex-32
A ball is thrown into the air from a cliff 20 m high. If the ball is
thrown with a velocity of 15 m/s at an angle of 30o below the
horizontal, calculate how far from the base of the cliff the ball
hits the ground.
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Physics Ex-32
Question-11
A projectile is fired into the air with
such initial velocity that its height is
12 m and its range is 48 m.
Determine the initial velocity of the
projectile.
Answer: 21.9 m/s [E 45o N]
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Question-12
Physics Ex-32
A helicopter is rising vertically at 15 m/s. When it is at a height
of 200 m above the ground, it fires a projectile horizontally with
a velocity of 50 m/s. Determine:
a) The time it takes the projectile to hit the ground.
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Question-12
Physics Ex-32
A helicopter is rising vertically at 15 m/s. When it is at a height
of 200 m above the ground, it fires a projectile horizontally with
a velocity of 50 m/s. Determine:
b) The horizontal displacement.
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