Projectile Fired at an Angle

← Projectile, Horizontal All Lessons Angle Problems →

Launching a projectile at an angle splits its initial velocity into horizontal (V_ix) and vertical (V_iy) 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 d_x)

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

Amazing Jump

By the way, this is a fake

Full Screen Version

Show Me The Physics Website

Fill in the Blank Notes

(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: V_ix and V_iy if θ = 0°.

↓

V_ix = 5 m/s, V_iy = 0

Given

Projectile fired at 5 m/s.
If θ = 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.

[ Flash ]
Show Me The Physics

[ Flash ]
Show Me The Physics Website

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

Finding Initial Horizontal & Vertical Components (parts)

[ Flash ]

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…

cosθ = A/H = V_ix/V

[ Flash ]

Cross multiply:

↓

Initial Horizontal Component of Velocity

V_ix = Vcosθ

(on reference table)

Since…

sinθ = Opp./Hyp. = V_iy/V

Cross multiply:

↓

Initial Vertical Component of Velocity

V_iy = Vsinθ

(on reference table)

During the time 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

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.

Vertical Component

↓

V_iy = Vsinθ
= (6.0 m/s)sin30.°

V_iy = 3.0 m/s up

Horizontal Component

↓

V_ix = Vcosθ
= (6.0 m/s)cos30.°

V_ix = 5.2 m/s across

Other Important Facts

d_x = V_xt (memorize)

a_y = -9.8 m/s² Ascending (down –)

a_y = +9.8 m/s² Descending (down +)

V_y at Peak = 0

Quick Review: Mystery Planet

t_peak = ½ t_total • V = at • d_x = V_xt

[ Open the bigger, full-screen version ]

Angles and Ranges

What angle produces the greatest range?

PelletierPhysics

↓

45 degrees

Projectile Range

[ HTML5 ]

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

[ HTML5 ]
Show Me The Physics Website

Given

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)

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 (d_x) to the greatest.

Newton's cannonball: cannonballs fired horizontally from a mountaintop at increasing speeds fall to the ground (A, B), circle Earth (C), trace an ellipse (D), or escape into space (E)

NYSSLS Reading Passage · 2D Motion

Newton's Cannonball: The Thought Experiment That Explained Orbits

Open Reading Passage → Regents Practice Version →

Check Your Understanding

5 quick questions — pick an answer to see if you’re right.

1. A baseball is thrown at 6.0 m/s at 30.° above horizontal. What is the initial vertical component of its velocity?

2. A projectile is launched at 10. m/s at 60.° above horizontal. What is its initial horizontal component?

3. Ignoring air resistance, what launch angle gives the greatest range over level ground?

4. A rock thrown at 30° lands a certain distance away. At the same speed, which other angle gives the same range?

5. At the very top of an angled projectile's path, which is true?

NYSSLS Regents Practice · Projectile Motion · Components

A Soccer Kick

A soccer player kicks a ball from level ground at 20. m/s at an angle of 30.° above the horizontal. Air resistance is negligible.

What are the initial horizontal and vertical components of the ball’s velocity?

▶ Want a challenge? Open 6 more Regents-style questions (harder · mixed formats)

Challenge score: 0 / 6

Select all that apply

C1. Place a check mark in two boxes to indicate the quantities that remain constant while the ball is in the air.

Multiple choice

C2. At the ball’s highest point, which statement is correct?

Substitute values

C3. Substitute numerical values into a mathematical representation that can be used to determine the maximum height the ball reaches above the ground. Then calculate the height.

h = ( m/s)²2( m/s²) = m

Support or Refute · Justify

C4. A student makes the following claim.

Claim: A ball kicked at 20. m/s at 60.° stays in the air twice as long as a ball kicked at 20. m/s at 30.°.

Place a check mark in either the Support or Refute box. Justify your response using a mathematical relationship.

Support Refute

Multiple choice

C5. The player kicks the ball at 20. m/s at 60.° instead. How does the range compare with the 30.° kick?

Constructed response

C6. A coach tells the player to kick at 45° instead of 30.° (same 20. m/s) to clear the ball downfield. Using the projectile model, identify one benefit and one drawback of the 45° kick.

Angle Problems →