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A soccer player kicks a soccer twice with the same force and
contact time. One kick was at an angle of 20 degrees and the
other kick was at an angle of 40 degrees. Which soccer ball went
further? (greater dx)

How many things would you have
to get right to make this work?

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Amazing_Jump

By the way, this is a fake

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Fill in the Blank Notes

2. Projectile fired at an angle
(not
0 or 90)

Projectile Path is Parabolic

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Baseball Throw
showmethephysics.com

Victoria Lollo - Class of 2007

Angle and Intitial Velocities

- Projectile fired at 5 m/s:

if Ө = 0

V _{ix} =
5 m/s, V _{iy} =
0

if Ө = 90

then .....

V _{ix} =
0 m/s and V _{iy} = 5
m/s

If angle is not 0 or 90 the
initial velocity is
part
vertical and part horizontal

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*** To understand this type of motion
we must breakup the
velocity
into
horizontal
and vertical parts (components)

Finding Initial Horizontal & Vertical Components
(parts)

V - velocity of projectile
fired

V_{ix} - initial V in x direction

V_{iy} - initial V in y direction

Use Trig. to Find V _{ix} and
V _{iy}

Since…

COSӨ =
A /H = V_{ix} /V

CROSS MULTIPLY:

Initial Horizontal
Component
of Velocity

V_{ix} = Vcos Ө
(on reference table)

Since…

sin Ө = Opp./Hyp. =
V _{iy} /V

CROSS MULTIPLY:

Initial
Vertical
Component of Velocity

V_{iy} = Vsin Ө
(on reference table)

During the times the ball is in the air,
how many times is the vertical velocity zero?

A bouncing ball captured with a stroboscopic flash at 25
images per second.

MichaelMaggs Edit by
Richard Bartz

Flash

2 times / At the Peak

Ex) A baseball is thrown
upward at an angle of 30.° and a velocity of 6.0 m/s.

Find the initial horizontal & vertical components
of the baseball's velocity.

Vertical Component

V_{iy} = VsinӨ

=(6.0 m/s)sin30.°

V_{iy}
= 3.0 m/s up

Horizontal Component

V_{ix} = Vcos Ө

=
(6.0 m/s) cos30. ^{°}

V_{ix}
= 5.2 m/s across

3. Other Important Facts

d_{x} =
V_{x} t

(memorize)

a_{y} = -9.8 m/s^{2}
Ascending
(down -)
a_{y} =+9.8 m/s^{2}
Descending
(down +)
V_{y} at Peak = 0

Angles and
Ranges

What angle produces the
greatest range?

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PelletierPhysics

45 degrees

Projectile Range

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Don Ion

Name another angle
that will give the same range (d_{x} )

55 degrees

35 degrees

65 degrees

25 degrees

55 degrees

35 degrees

20 degrees

70 degrees

Minimum Range

0°, 90°

Maximum Range

45°

Angle with Longest
Time in Air?

90 degrees

Angle & Components

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Ex)
Which angle of projection causes a projectile to stay in the air longer?

50 or 70 degrees?

70 degrees,
(closest to 90,
longer time in air)

Ranking
Task

1. A rock is thrown at various angles but with the
same initial velocity .

2° 70°
20° 5° 60°

Rank the angles above from smallest horizontal displacement
(dx ) to the greatest

Projectile
at an Angle
- Word Problems

[AP ]

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