Projectile Motion

Projectile Fired at an Angle

Breaking initial velocity into horizontal & vertical components

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Launching a projectile at an angle splits its initial velocity into horizontal (Vix) and vertical (Viy) components — together they determine how far and how long it flies.

 

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

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

Amazing Jump

By the way, this is a fake

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Fill in the Blank Notes

Projectile Fired at an Angle

(not 0° or 90°)

Projectile Path is Parabolic

Baseball Throw
showmethephysics.com

Victoria Lollo - Class of 2007

Angle and Initial Velocities

Projectile fired at 5 m/s:

Given

Projectile fired at 5 m/s.
Find: Vix and Viy if θ = 0°.

↓

Vix = 5 m/s, Viy = 0

Given

Projectile fired at 5 m/s.
If θ = 90°, then…?

↓

Vix = 0 m/s and Viy = 5 m/s

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

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Vix and Viy components diagram
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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)

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V - velocity of projectile fired

Vix - initial V in x direction

Viy - initial V in y direction

Use Trig. to Find Vix and Viy

Since…

cosθ = A/H = Vix/V

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Cross multiply:

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Initial Horizontal Component of Velocity

Vix = Vcosθ

(on reference table)

Since…

sinθ = Opp./Hyp. = Viy/V

Cross multiply:

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Initial Vertical Component of Velocity

Viy = Vsinθ

(on reference table)

Projectile at an angle diagram

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

Bouncing ball captured with a stroboscopic flash
A bouncing ball captured with a stroboscopic flash at 25 images per second.
MichaelMaggs Edit by Richard Bartz

Flash

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2 times / At the Peak

Given

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.

Projectile at an angle diagram

Vertical Component

↓

Viy = Vsinθ = (6.0 m/s)sin30.°

Viy = 3.0 m/s up

Horizontal Component

↓

Vix = Vcosθ = (6.0 m/s)cos30.°

Vix = 5.2 m/s across

Other Important Facts

dx = Vxt  (memorize)

ay = -9.8 m/s² Ascending (down –)

ay = +9.8 m/s² Descending (down +)

Vy at Peak = 0

Angles and Ranges

What angle produces the greatest range?

PelletierPhysics

↓

45 degrees

Projectile Range

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Don Ion

Name another angle that will give the same range (dx)

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55 degrees

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35 degrees

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65 degrees

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25 degrees

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55 degrees

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35 degrees

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20 degrees

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70 degrees

Minimum Range

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0°, 90°

Range vs angle diagram

Maximum Range

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45°

 45 degrees gives maximum distance

Angle with Longest
Time in Air?

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90 degrees

Angle & Components

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Given

Ex) Which angle of projection causes a projectile to stay in the air longer?
50 or 70 degrees?

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70 degrees

(closest to 90°, longer time in air)

Given

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

2°   70°   20°  5°  60°

Find: rank the angles above from smallest horizontal displacement (dx) to the greatest.

Projectile at an Angle - Word Problems

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Angle Problems →