Kinematics

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14 Νοε 2013 (πριν από 3 χρόνια και 6 μήνες)

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Kinematics

Geometry of Motion

What is Kinematics?

Kinematics

is the study of the geometry
of motion and is used to relate
displacement, velocity, acceleration and
time without reference to the cause of
motion.


Projectile Motion Assumptions

The variations of gravity (g) with

respect to differing altitudes is



negligible and can be ignored.

Gravity is constant:





or


Projectile Motion

First step:

To analyze projectile motion, separate

the two
-
dimensional motion into

vertical and horizontal components.


Projectile Motion

Horizontal Direction, x
, represents the

range, or distance the

projectile

travels.


Vertical Direction, y,

represents the

altitude, or height, the projectile

reaches.



Projectile Motion Formulas

Initial Velocity (v
i
) can be broken
down into its x and y components:



Projectile Motion Formulas

Going one step further:


There is a right triangle relationship between
the velocity vectors


Use Right Triangle
Trigonometry to solve for each of them.

Right triangle:


A triangle with a
90
°

angle.





Right Triangle Review:

Opposite


side,
O

Adjacent

side,
A

θ
°

90
°

Sides:


Hypotenuse,
H


Adjacent side,
A


Opposite side,
O

Trigonometric Functions:



sin
θ
°

=
O

/
H



cos θ
°

=
A

/
H



tan
θ
°

=
O

/
A



Trigonometric Functions:


Projectile Motion Problem

A ball is fired from a device, at a rate
of 160 ft/sec, with an angle of 53
degrees to the ground.







Projectile Motion Problem



Find the x and y components of V
i
.



At the highest point (the vertex) what

is the altitude (h) and how much

time has elapsed?



What is the ball’s range (the distance

traveled horizontally)?






Projectile Motion Problem


Find the x and y components of V
i
.

V
i

= initial velocity = 160 ft/sec


Projectile Motion Problem


Find the x and y components of V
i
.


Projectile Motion Problem


Find the x and y components of V
i
.


Projectile Motion Problem


At the highest point (the vertex), what is

the

altitude (h) and how much time has

elapsed?

Start by solving for time.



Projectile Motion Problem


At the highest point (the vertex), what is the

altitude (h) and how much time has

elapsed?

Now using time, find h (y
max
).



Projectile Motion Problem


What is the ball’s range (the distance

traveled horizontally)?


It takes the ball the same amount of time to reach its
maximum height as it does to fall to the ground, so total time
(t) = 8 sec. Using the formula:

Projectile Motion Problem
-
2

A golf ball is hit at an angle of 37
degrees above the horizontal with a
speed of 34 m/s. What is its maximum
height, how long is it in the air, and how
far does it travel horizontally before
hitting the ground?