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### Transcript of Angular Projectile Motion

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ANGULAR PROJECTILEMOTION

How does a javelin

move?

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Throwing and falling.

Carry out the following simple experimentsto understand motion through the air.

From a high point drop a ball, time its falland describe its motion.

Throw a ball vertically upwards anddescribe the motion.

Project a ball horizontally from a high pointand describe its motion.

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Important facts!!

A falling object has only verticalcomponents of velocity.

An object thrown vertically upwards only

has vertical components of velocity. Objects thrown horizontally at a height

above the ground or objects thrown up-

and-sideways simultaneously have verticaland horizontal components of velocity.

The pathway followed by an object moving

through the air is called a trajectory.

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Falling bodies

Projectile motion

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The bullet has two components to its velocity horizontal and vertical.

The bullet continues with a constant horizontalvelocity, until it reaches the ground. The

horizontal distance moved is given by x = vixt

The vertical motion of the ball is due to the forceof gravity downward acceleration of 10m.s-2.

The vertical distance fallen is given byx =vit + gt

2 ,where vi, the vertical initial velocity = 0.

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Distance (m)

Height

(m)

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Projectiles fired at an angle

Notice how the components change/stay the

same.

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The bullet has two components to its velocity horizontal and vertical.

The bullet continues with a constant horizontalvelocity, until it reaches the ground. The horizontaldistance moved is given by x = uxt

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Describe the motion

The vertical motion of the ball is due to the forceof gravity downward acceleration of 10m.s-2.

The vertical distance fallen is given by

x = vit + gt2 , where vi, the vertical initialvelocity > 0

Heightin

m

Distance in m

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A football is kicked with a speed of 25 m.s-1

atan angle of 30o to the horizontal.Neglecting air resistance determine:

(a) The time of flight for the football.(b) The maximum height reached by the

football.

(c) The horizontal range of the football.

(2.55 s)

(7.97 m)

(55.2 m)

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A crate of supplies for a scientific expeditionto Greenland is being dropped by

plane. When the supplies are dropped, theplane is traveling at 40 m.s-1 horizontally at aheight of 50 m. Sadly the parachute fails to

open and the package falls to the ground at9.8 m/s2.

Find the horizontal distance travelled by thepackage as it falls given that it hits the groundright at the feet of the scientific party.

(127.8 m)

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A stone is thrown horizontally from the topof a vertical cliff. Given that the initial

velocity of the stone is 20 m.s-1

and that ithits the horizontal ground below the cliff 3seconds later, calculate:(a) The horizontal distance travelled by the stone

from the foot of the cliff.

(b) The height of the cliff.

(c) The velocity of the stone just before it hits theground.

(60 m)

(44.1 m)

(35.6 m/s at an angle of 55.8o

below the horizontal)

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EXTENSION QUESTION

A stone is thrown vertically upwards with avelocity of 29.4 m.s-1 from the edge of a cliff78.4 m high. The stone falls so that it justmisses the edge of the cliff and falls to theground at the foot of the cliff.

Determine the time taken by the stone to

reach the ground.

Assume that the acceleration due to gravity is 9.8ms-2. (Ans = 8 s)

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What must you be able to do?

Determine the path of a projectile firedhorizontally calculate the distancetravelled and the velocity at each point in

its path.

Determine the path of a projectile fired atsome other angle calculate the distance

travelled and the velocity at each point inits path.