High School

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Physics Ex-32

Projectile motion is the vectorial sum of two independent velocities,a horizontal component and a vertical component.

The horizontal component velocity (VH) is constant throughout themotion while the vertical component velocity (VV) equals free fall.

The actual or instantaneous velocity at any point along the parabolicpath is tangent to the parabola and equal to the vectorial sum of thehorizontal and vertical component velocities.

In solving problems on projectile In solving problems on projectile motion, work out the vertical and motion, work out the vertical and horizontal component velocitieshorizontal component velocities

separatelyseparately as if they were two as if they were two separate problems.separate problems.

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NOTE

Physics Ex-32Question-1

Two stones, A and B, are used in an experiment. At the same timethat stone A is dropped, stone B is thrown down horizontally witha velocity of 25 m/s. For each second of fall, fill in the velocitiesof both stones, as indicated. (You need not include the units)

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010

20

30

40

50

025

2510

2520

2530

2540

2550

Use 10 m/s2 for the acceleration due to gravity.

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Physics Ex-32Question-2

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A stone is dropped from a balcony 20 m high. How long doesit take the stone to reach the ground?

Physics Ex-32Question-3

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A ball is thrown horizontally from a 20 m high cliff witha velocity of 10 m/s. How far from the base of the cliffdoes the ball land?

NOTEThe time it takes the ballto strike the ground is the

same time it takes an object to fall freely 20 m.

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Step-1: Calculation of falling time

Step-2: Calculation of range

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Physics Ex-32Question-4

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A ball is thrown in the air with a velocity of 20 m/s at an angleof 60o from the horizontal. Calculate:

NOTEThe vertical component of the

velocity is identical to shooting an object vertically

upwards.

a) How high it rises (the height).

Physics Ex-32Question-4

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A ball is thrown in the air with a velocity of 20 m/s at an angleof 60o from the horizontal. Calculate:

NOTEThe horizontal component of

the velocity is the same throughout the flight and is thus an average velocity.

b) How far it travels (the range).

Multiply by 2 to obtain total time.

Physics Ex-32Question-5

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A ball is thrown in the air with a velocity of 20 m/s at an angleof 45o from the horizontal. Calculate:

NOTEThe vertical component of the

velocity is identical to shooting an object vertically

upwards.

a) How high it rises (the height).

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Physics Ex-32Question-5

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A ball is thrown in the air with a velocity of 20 m/s at an angleof 45o from the horizontal. Calculate:

b) How far it travels (the range).

NOTEThe 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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Physics Ex-32Question-6

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A ball is thrown in the air with a velocity of 20 m/s at an angleof 30o from the horizontal. Calculate:

NOTEThe vertical component of the

velocity is identical to shooting an object vertically

upwards.

a) How high it rises (the height).

Physics Ex-32Question-6

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A ball is thrown in the air with a velocity of 20 m/s at an angleof 30o from the horizontal. Calculate:

b) How far it travels (the range).

NOTEThe horizontal component of

the velocity is the same throughout the flight and is thus an average velocity.

Physics Ex-32Question-7

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The table below summarizes the answers from the previous threequestions (4, 5 and 6):

Initial velocity Angle Height Range

Question-4 20 m/s 60o 15 m 35 m

Question-5 20 m/s 45o 10 m 40 m

Question-6 20 m/s 30o 5 m 35 m

Which angle produces the greatest height? a) 60o

Which angle produces the greatest range? b) 45o

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REMEMBERREMEMBER

The greatest The greatest rangerange is always is always produced by an angle of 45produced by an angle of 45oo..

Physics Ex-32Question-8

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A cannon ball is fired into the air at an angle of 40o from thehorizontal and rises 5 m. Calculate its range.

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Time = 1 s going up + 1 s coming down

Physics Ex-32

A ball is thrown into the air from a cliff 20 m high. If the ball isthrown with a velocity of 15 m/s at an angle of 30o above thehorizontal, calculate how far from the base of the cliff the ballhits the ground.

Question-9

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Physics Ex-32

A ball is thrown into the air from a cliff 20 m high. If the ball isthrown with a velocity of 15 m/s at an angle of 30o below thehorizontal, calculate how far from the base of the cliff the ballhits the ground.

Question-10

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Physics Ex-32Question-11

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A projectile is fired into the air withsuch initial velocity that its height is 12 m and its range is 48 m.

Determine the initial velocity of theprojectile.

Answer: 21.9 m/s [E 45o N]

Physics Ex-32Question-12

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A helicopter is rising vertically at 15 m/s. When it is at a heightof 200 m above the ground, it fires a projectile horizontally witha velocity of 50 m/s. Determine:

The time it takes the projectile to hit the ground.a)

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Physics Ex-32Question-12

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A helicopter is rising vertically at 15 m/s. When it is at a heightof 200 m above the ground, it fires a projectile horizontally witha velocity of 50 m/s. Determine:

The horizontal displacement.b)

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